⭕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
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Answered by
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)
Answered by
1
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
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