Question

Find value of a & b so that the polynomial x^3 -10x^2 +ax +b is exactly divisible by (x-1) as well as (x-2).​

Answer 1

Explanation:

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Answer 2

$\huge \mathfrak{answer}$

Given : Polynomial x⁴+ax³ −7x ²−8x+b is exactly divisible

by (x+2) as well (x+3)

⇒x=−2,−3 are the roots of polynomial

∴(−2) ⁴+a(−2) ³−7(−2) ²−8(−2)+b=0

16−8a−28+16+b=0

−8a+b=−4 ... (I)

(−3) ⁴+a(−3) ³−7(−3)² −8(−3)+b=0

81−27a−63+24+b=0

−27+b=−42 .... (II)

(I) - (II)

a=2

put a=2 in equation (I)

−16+b=−4

b=−4+16

b=12

∴a=2,b=12

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