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

Step-by-step 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.

3x2 + 6x + 4 = 0

Step-by-step explanation:

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)

i think the length is 12 and the width is 17