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).​


⭞ ℂ​

Answer 1

Answer :

Given : Polynomial x

4

+ax

3

−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)

Answer 2

Given : Polynomial x

4

+ax

3

−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)

Ref. Image

a=2

put a=2 in equation (I)

−16+b=−4

b=−4+16

b=12

∴a=2,b=12