Question

find the value of a & b so that x^3+10x^2+ax+b is exactly divisible by x-1 as well as x+2

Answer 1

here's your ans hope it helps!

Answer 2

Heya !!!

X-1 = 0

X = 2

and,

X+2 = 0

X = -2

P(X) = X³+10X²+AX+B

P(1) = (1)³ + 10 × (1)² + A × 1 + B

=> 1 + 10 + A + B = 0

=> A + B + 11 = 0

=> A + B = -11----------(1)

Also,

X = -2

P(-2) => (-2)³ + 10 × (-2)² + A × -2 + B

=> -8 + 10 × 4 - 2A + B

=> -8 + 40 - 2A + B = 0

=> -2A + B +32 = 0

=> -2A + B = -32

=> 2A - B = 32----------(2)

From equation (1) we get,

A + B = -11

A = (-11-B)-----------(3)

Putting the value of A in equation (2)

2A - B = 32

2 × (-11-B) - B = 32

-22 - 2B - B = 32

-3B - 22 = 32

-3B = 32+22

-3B = 52

B = -54/3 = -18

Putting the value of B in equation (3)

A = -11 - B = -11 -18 = -29


Hence,


A = -29 and B = -18

HOPE IT WILL HELP YOU.... :-)