Question

II. Characterize the rootts of the following quadratic equations using the discriminant. Use the example below.

Example: 2x² + 8x+6=0
a = 2 b= 8 c= 6
b²-4ac (8²) -4(2)6)
=64-48
= 16 (greater than zero) - roots are real and unequal.
Given: x2-16x + 64 = 0
Given: 3x2 + 6x + 4 = 0
Given: 2x2 - 10x + 6 = 0​

Answer 1

3x2 + 6x + 4 = 0

Explanation:

Answer 2

Explanation:

Note: x2-16x + 64 = 0 should be written x^2 - 16x + 64 = 0. The coefficients are a = 1, b = -16 and c = 64. The discriminant, b^2 - 4ac, is (-16)^2 - 4(1)(64) = 0. A zero discriminant indicates that there are two equal, real roots.

Note: 3x2 + 6x + 4 = 0 => 3x^2 + 6x + 4. The coefficients a, b and c are {3, 6, 4} and so the discriminant is b^2 - 4ac, or 36 - 48, or -12. A negative discriminant indicates that there are two complex, unequal roots.

Note: 2x2 - 10x + 6 = 0 => x^2 - 5x + 3, whose coefficients are {1, -5, 3}. The discriminant is (-5)^2 - 4(1)(3) = 13. A positive discriminant indicates that there are two unequal, real roots.