Q. 275.0( 1 Vote )

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Answer :

Let p(x) = x3 + 10x2 + px + q


As (x – 1) and (x + 2) are factors of p(x) hence each will divide p(x) leaving remainder as 0


Let us use the remainder theorem which states that if (x – a) divides a quadratic polynomial p(x) then p(a) = 0 so we have p(1) = 0 and p(–2) = 0


p(1) = 0


13 + 10(1)2 + p(1) + q = 0


1 + 10 + p + q = 0


p + q = –11


q = –11 – p …(i)


p(–2) = 0


(–2)3 + 10(–2)2 + p(–2) + q = 0


–8 + 40 – 2p + q = 0


32 – 2p + q = 0


Substituting value of q from (i)


32 – 2p – 11 – p = 0


21 – 3p = 0


3p = 21


p = 7


Substitute p in (i)


q = – 11 – 7


q = –18


Hence value of p and q are 7 and –18 respectively


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