Question

if (x+1) is a factor of x^3+px+q and x^2+p'x+q' then find the value of x​

Answer 1

Step-by-step explanation:

What is the value of p and q if (x + 1) and (x + 2) are the factors of x^3 + 3x^2 – 2px + q?

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Given that

(x+1)and(x+2) are two factors of cubic polynomial: x³+3x²-2px+q

Since it is a cubic Polynomial; let us assume its third factor be (x+k)

Hence we should have

(x+1)(x+2)(x+k)= x³+3x²-2px+q

On multiplying the factors on LHS and arranging the term of like power; we get

x³+x²(k+3)+x(3k+2)+2k= x³+3x²-2px+q

Comparing the coefficients

K+3=3→k=0

3k+2=-2p→2=-2p→p=-1

&

2k=q →q=0

Thus

P=-1 and q=0

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