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.
Watch this video for solving with the quadratic formula.
Watch this video for a review of using the discriminant.
1

Match the discriminant with the indicated type of roots.

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

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

Find the discriminant of

x2+12x-8 = 0

Enter your answer as a number, no spaces.

1

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.

1

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

Enter your answer as a number, no spaces.

1

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.

1

Find the discriminant of

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

Enter your answer as a number, no spaces.

1

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".

1

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

Enter your answer as a number, no spaces.

1

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.

1

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

Enter your answer as a number, no spaces.

1

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.

1

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

1

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

Hint: Check this with #1!

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.