P4.4: Quadratic Formula and the Discriminant

Last updated almost 4 years ago

14 questions

Note from the author:

Watch this video for solving with the quadratic formula.
Watch this video for a review of using the discriminant.

Instructions

Watch this video for solving with the quadratic formula.
Watch this video for a review of using the discriminant.

P4.4: Quadratic Formula and the Discriminant

Last updated almost 4 years ago

14 questions

Note from the author:

Watch this video for solving with the quadratic formula.
Watch this video for a review of using the discriminant.

Instructions

Watch this video for solving with the quadratic formula.
Watch this video for a review of using the discriminant.

Match the discriminant with the indicated type of roots.

This won't turn green until you have them ALL right.

Draggable item		Corresponding Item
discriminant is negative		2 real rational roots
discriminant is 0		2 real irrational roots
discriminant is positive, but not a perfect square		1 unique root
discriminant is a positive perfect square		2 nonreal roots

Find the discriminant of

x2+12x-8 = 0

Enter your answer as a number, no spaces.

Solve

x2+12x-8=0.

Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.

Find the discriminant of
13x^{2}-16x=x^{2}-x

Enter your answer as a number, no spaces.

Solve
13x^{2}-16x = x^{2}-x.

Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals. No decimals.

Find the discriminant of

8x^{2}+15x = 7x-4

Enter your answer as a number, no spaces.

Solve
8x^{2}+15x = 7x-4

Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.

If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.

This one will be "ugly".

Find the discriminant of
5x^{2}+1 = 4x -7

Enter your answer as a number, no spaces.

Solve
5x^{2}+1 = 4x-7

Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.

If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.

Find the discriminant of
-2x^{2}+24 = 8x

Enter your answer as a number, no spaces.

Solve
-2x^{2}+24 = 8x

Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.

If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.

The discriminant of a quadratic equation is 122. Which describes the number and type of roots for that equation?

The discriminant of a quadratic equation is -36. Which describes the number and type of roots for that equation?

Hint: Check this with #1!

REVIEW
Solve by square roots.

2(x+1)^{2}+5 = -3

Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.
If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.

P4.4: Quadratic Formula and the Discriminant

P4.4: Quadratic Formula and the Discriminant

Match the discriminant with the indicated type of roots.This won't turn green until you have them ALL right.

Find the discriminant of x2+12x-8 = 0Enter your answer as a number, no spaces.

Solve x2+12x-8=0.Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.

Find the discriminant of13x^{2}-16x=x^{2}-xEnter your answer as a number, no spaces.

Solve13x^{2}-16x = x^{2}-x.Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals. No decimals.

Find the discriminant of8x^{2}+15x = 7x-4Enter your answer as a number, no spaces.

Solve8x^{2}+15x = 7x-4Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.This one will be "ugly".

Find the discriminant of5x^{2}+1 = 4x -7Enter your answer as a number, no spaces.

Solve5x^{2}+1 = 4x-7Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.

Find the discriminant of-2x^{2}+24 = 8xEnter your answer as a number, no spaces.

Solve-2x^{2}+24 = 8xEnter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.

The discriminant of a quadratic equation is 122. Which describes the number and type of roots for that equation?

The discriminant of a quadratic equation is -36. Which describes the number and type of roots for that equation?Hint: Check this with #1!

REVIEW Solve by square roots.2(x+1)^{2}+5 = -3Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.

Match the discriminant with the indicated type of roots.This won't turn green until you have them ALL right.

Find the discriminant of x2+12x-8 = 0Enter your answer as a number, no spaces.

Solve x2+12x-8=0.Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.

Find the discriminant of13x^{2}-16x=x^{2}-xEnter your answer as a number, no spaces.

Solve13x^{2}-16x = x^{2}-x.Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals. No decimals.

Find the discriminant of8x^{2}+15x = 7x-4Enter your answer as a number, no spaces.

Solve8x^{2}+15x = 7x-4Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.This one will be "ugly".

Find the discriminant of5x^{2}+1 = 4x -7Enter your answer as a number, no spaces.

Solve5x^{2}+1 = 4x-7Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.

Find the discriminant of-2x^{2}+24 = 8xEnter your answer as a number, no spaces.

Solve-2x^{2}+24 = 8xEnter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.

The discriminant of a quadratic equation is 122. Which describes the number and type of roots for that equation?

The discriminant of a quadratic equation is -36. Which describes the number and type of roots for that equation?Hint: Check this with #1!

REVIEW Solve by square roots.2(x+1)^{2}+5 = -3Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.

Match the discriminant with the indicated type of roots.

This won't turn green until you have them ALL right.

Find the discriminant of

x2+12x-8 = 0

Enter your answer as a number, no spaces.

Solve

x2+12x-8=0.

Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.

Find the discriminant of
13x^{2}-16x=x^{2}-x

Enter your answer as a number, no spaces.

Solve
13x^{2}-16x = x^{2}-x.

Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals. No decimals.

Find the discriminant of

8x^{2}+15x = 7x-4

Enter your answer as a number, no spaces.

Solve
8x^{2}+15x = 7x-4

Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.

If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.

This one will be "ugly".

Find the discriminant of
5x^{2}+1 = 4x -7

Enter your answer as a number, no spaces.

Solve
5x^{2}+1 = 4x-7

Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.

If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.

Find the discriminant of
-2x^{2}+24 = 8x

Enter your answer as a number, no spaces.

Solve
-2x^{2}+24 = 8x

Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.

If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.

The discriminant of a quadratic equation is -36. Which describes the number and type of roots for that equation?

Hint: Check this with #1!

REVIEW
Solve by square roots.

2(x+1)^{2}+5 = -3

Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.
If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.

Match the discriminant with the indicated type of roots.

This won't turn green until you have them ALL right.

Find the discriminant of

x2+12x-8 = 0

Enter your answer as a number, no spaces.

Solve

x2+12x-8=0.

Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.

Find the discriminant of
13x^{2}-16x=x^{2}-x

Enter your answer as a number, no spaces.

Solve
13x^{2}-16x = x^{2}-x.

Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals. No decimals.

Find the discriminant of

8x^{2}+15x = 7x-4

Enter your answer as a number, no spaces.

Solve
8x^{2}+15x = 7x-4

Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.

If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.

This one will be "ugly".

Find the discriminant of
5x^{2}+1 = 4x -7

Enter your answer as a number, no spaces.

Solve
5x^{2}+1 = 4x-7

Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.

If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.

Find the discriminant of
-2x^{2}+24 = 8x

Enter your answer as a number, no spaces.

Solve
-2x^{2}+24 = 8x

Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.

If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.

The discriminant of a quadratic equation is -36. Which describes the number and type of roots for that equation?

Hint: Check this with #1!

REVIEW
Solve by square roots.

2(x+1)^{2}+5 = -3

Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.
If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.