Find the value of p and q if (x+1)and (x+2) are the factors of x^3+3x^2-2px+q
Answers
Answered by
4
Step-by-step explanation:
if (x-1) and (x+2) are factors of equation
f(x) = x^3 + px^2 - 7x + q = 0 find the
values of p and q.
(x-1)(x+2) = x^2 + x - 2
Divide by x^2 + x - 2:
x^3 + px^2 - 7x + q | x
x^3 + x^2 - 2x
–––––––––––––––––––
(p-1)x^2 - 5x + q | (p-1)
(p-1)x^2 + (p-1)x - 2(p-1)
––––––––––––––––––––––
(-p+1-5)x + 2p -2 + q = 0
(-p-4)x + (2p-2+q) = 0
-p-4 = 0 ==> p = -4
2p-2+q = 0 = -8-2+q ==> q = 10
Check:
Quotient is third factor: x + (p-1) = x - 5.
f(x) = (x-1)(x+2)(x-5) = (x^2 + x - 2)(x-5)
= x^3 + x^2 - 2x
- 5x^2 - 5x + 10
= x^3 - 4x^2 - 7x + 10 √
Similar questions