Question

Find the sum and product of the roots for the equation −9x^2−8x+15=0, where a=−9, b=−8, and c=15.

a) Sum of the roots: 8/9; Product of the roots: -15/9
b) Sum of the roots: 8/9; Product of the roots: 15/9
c) Sum of the roots: -8/9; Product of the roots: 15/9
d) Sum of the roots: -8/9; Product of the roots: -15/9

Answer 1

For the quadratic equation −9x^2−8x+15=0, the sum of the roots is 8/9, and the product of the roots is -15/9, derived using Vieta's formulas by substituting the coefficients a=-9, b=-8, and c=15.

Step-by-step explanation:

The given equation −9x2−8x+15=0 is a quadratic equation of the form ax2+bx+c=0. To find the sum and product of its roots, we can use the formulas that are derived from Vieta's formulas:

• Sum of the roots (S) = -b/a
• Product of the roots (P) = c/a

Substituting the given coefficients a=-9, b=-8, and c=15 into these formulas, we get:

• S = -(-8)/(-9) = 8/9
• P = 15/(-9) = -15/9

Therefore, the correct answer for the sum and product of the roots of the equation −9x2−8x+15=0 is:

• Sum of the roots: 8/9
• Product of the roots: -15/9