Question

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Find the value of a if x minus A is a factor of x cube -ax square + 2 X + a - 1

Answer 1

Answer:

Step-by-step explanation:

We need to check if (2x-3) is a factor of the polynomial 2x³-9x²+x+12

Fir.st equate 2x-3 to 0 and find value of x.

2x - 3 = 0

⇒ 2x = 3

⇒ x = 3/2

If x=3/2 is a root of the polynomial, then (2x-3) is a factor.

at x=3/2, value of polynomial is

2(3/2)³ - 9(3/2)² + 3/2 + 12

= 2×(27/8) - 9×(9/4) + 3/2 + 12

= 27/4 - 81/4 + 3/2 + 12

= (27 - 81 + 6 + 48)/4

= (81-81)/4

= 0

So 3/2 is a root of the polynomial. Hence (2x-3) is a factor of the polynomial.

Answer 2

Answer:

Let p(x)=x3+ax2+2x+b

(x+1) and (x+2) are the factors of p(x)

p(-1)=0

(-1)3+a(-1)2+2(-1)+b=0

-1+a-2+b=0

a+b-3=0 ..(1)

p(-2)=0

(-2)3+a(-2)2+2(-2)+b=0

-8+4a-4+b=0

4a+b-12=0 ..(2)

Equating both the equations

a+b-3=4a+b-12

-3+12=4a-a+b-b

9=3a

a=3

a+b-3=0

3+b-3=0

b=0