karlaceron04
contestada

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?

Respuesta :

mhanifa

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

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