Question

Find the value of p and q if ( x-1)^2 is a factor of x^3+4x^2-(2p-q)x+pq

Answer 1

Answer:f (x-1) and (x+2) are factors of equation

if(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

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(p-1)x^2 -       5x +     q    | (p-1)

(p-1)x^2 + (p-1)x - 2(p-1)

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(-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 √

Step-by-step explanation: