Question

The quadratic function g(x) = ax^2 + bx + c has the complex roots (-5+9i) and (-5-9i). (you may assume that a = -1) what is the value of b and c?

Answer 1

Answer:

• b = -10, c = -106

Step-by-step explanation:

Given

Quadratic function

• g(x) = ax^2 + bx + c

with the roots:

• (-5+9i) and (-5-9i)

To find

• b and c if a = -1

Solution

As we know the sum of the roots is -b/a and the product of the roots is c/a. Substituting values and solving for b and c:

• (-5 + 9i) + (-5 - 9i) = -b/-1
• -10 = b
• b = -10

And

• (-5 + 9i)(-5 - 9i) = c/-1
• (-5)² - (9i)² = -c
• 25 - 81(-1) = -c
• - c = 25 + 81
• - c = 106
• c = -106

g(x) = -x² -10x - 106