Question

Find the value of p and q if (x-1) and (x+2) are the factors of x^3 +3x^2 -2p +q

Answer 1

Answer:

here is your answer mate...

Step-by-step explanation:

x-1 and x+1 are factors of x⁴+px³+2x²-3x+q

x-1 = 0 ; x = 1

x+1 = 0 ; x = -1

Put x = ±1 to know the values of p and q

Put x = 1

(1)⁴+p(1)³+2(1)²-3(1)+q = 0

1+p+2-3+q = 0

p+q+3-3 = 0

p+q = 0 -------(1)

Put x = -1,

(-1)⁴+p(-1)³+2(-1)²-3(-1)+q = 0

1-p+2+3+q = 0

-p+q+3+3 = 0

-p+q = -6 ------(2)

(1) + (2)

p + q = 0

-p + q = -6

---------------

2q = -6

q = -6/2

q = -3

p+q = 0

p+(-3) = 0

p = 3

Therefore, p = 3 and q = -3

Hope it helps

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