P4.4: Quadratic Formula and the Discriminant
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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.
Match the discriminant with the indicated type of roots.
This won't turn green until you have them ALL right.
| Draggable item | arrow_right_alt | Corresponding Item |
|---|---|---|
discriminant is a positive perfect square | arrow_right_alt | 2 real rational roots |
discriminant is negative | arrow_right_alt | 2 real irrational roots |
discriminant is positive, but not a perfect square | arrow_right_alt | 1 unique root |
discriminant is 0 | arrow_right_alt | 2 nonreal roots |
1
Find the discriminant of
x2+12x-8 = 0
Enter your answer as a number, no spaces.
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.
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 of13x^{2}-16x=x^{2}-x
Enter your answer as a number, no spaces.
Find the discriminant of
13x^{2}-16x=x^{2}-x
Enter your answer as a number, no spaces.
1
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.
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.
Find the discriminant of
8x^{2}+15x = 7x-4
Enter your answer as a number, no spaces.
1
Solve8x^{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".
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 of5x^{2}+1 = 4x -7
Enter your answer as a number, no spaces.
Find the discriminant of
5x^{2}+1 = 4x -7
Enter your answer as a number, no spaces.
1
Solve5x^{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.
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.
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.
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?
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!
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.
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.