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Answer:
c) x^2 - 9x - 22 = 0
Step-by-step explanation:
Consider the generic case ...
(x -a)(x -b) = 0 . . . . . . . has solutions x=a, x=b
Multiplying this out gives ...
x^2 -ax -bx +ab = 0
x^2 -(a+b)x +ab = 0
This tells you ...
- the coefficient of x is the opposite of the sum of the roots
- the constant is the product of the roots
The sum of roots is 11 +(-2) = 9, and the opposite of that is -9. You are looking for an equation with the term -9x. (Choice C matches)
The product of roots is (11)(-2) = -22. You are looking for an equation with a constant of -22. (Choice C matches that, too.)
The equation is ...
x^2 -9x -22 = 0
