Question

find the value of a and b so that the polynomial 2xcube plus ax square plus bx plus 6 us divisible by x square plus x minus 6
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Answer 1

Answer:

Answer is :- 8,12

Step-by-step explanation:

f(x)=2x

3

+ax

2

+bx−6

(x−1) is a factor

∴f(1)=0⇒2+a+b=6

⇒a+b=4→1

and f(x) leaves remainder 2 on being divided by (x−2)

∴f(2)=2

⇒2×2

3

+a×2

2

+b×2−6=2

⇒4a+2b+16−6=2

⇒4a+2b=2−10=−8

⇒2a+b=−4

Solving 1 and 2

2a+b=−4

a+b=4

−−−

a=−8

a+b=4

−8+b=4

b=4+8=12

∴a=−8;b=12

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