Question

Please solve this question quickly

Answer 1

x^2+x-12 = (x-3)(x+4)

According to the given condition,

x^2+x-12 = (x-3)(x+4) is a factor of x^3+ax^2+bx-84 = f(x).

Hence, f(3) = f(-4) = 0

Therefore, 

27+9a+3b-8=0  or 3a+b-19=0

-64 + 16a-4b-8=0 or 4a-b-37=0

Adding these two equations, we get, 7a - 56 = 0 or a = 8

So, b = 19-24 = -5

Hope it helps.

Answer 2

Howdy!!

your answer is -----

Firstly, we factories x^2+x-12

x^2 + x - 12 = 0

=> x^2 +4x - 3x - 12 = 0

=> x (x+4) - 3(x+4) = 0

=> (x+4) (x-3) = 0

=> x = - 4 Or x = 3

since, x^2+x-12 is exactly divided p(x)=x^3+ax^2+bx-8.

so, when we take x = -4

then , p(-4) = 0

=> -4^3 + a(-4)^2+b×-4 -8 = 0

=> -64 + 16a - 4b - 8 = 0

=> 16a - 4b = 72

=> 4a - b = 18 ...(1)

when , x = 3
then, also p(3) = 0

=> 3^3 + a ×3^2 + b×3 -8 = 0

=> 27 + 9a + 3b - 8 = 0

=> 9a + 3b = -19 .....(2)

now, multiply equation (1) by 3 and (2) by 1

so, 12a - 3b = 54 .. (3)

9a + 3b = -19 ..(4)

adding equation (3) and (4), we get

21a = 35

=> a = 35/21

Now, put this value in equation (4),we get

9×35/21 + 3b = -19

=> 315/21 + 3b = -19

=> -3b = 315/21 + 19

=> -3b = 714/21

=> -3b = 34

=> b = -34/3


hence , a = 35/21 and b = -34/3

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hope it help you