Question

If x^2-3x+3 is a factor of x^4-ax+b than find the value of a and b

Answer 1

$\underline{ \underline{ \tt \: question}}$

If x^2 -3x +3 is a factor of x^4 - ax + b then find the value of a and b.

$\underline{ \underline{ \tt \: solution}}$

If x^2 -3x +3 is a factor of x^4 - ax + b then,

on division the remainder will be zero.

on division we will get

remainder = - x (a - 9) + (b -18)

remainder = x ( 9 - a) + ( b - 18 )

equalising it with zero

x ( 9 - a) + ( b - 18 ) = 0

x ( 9 - a) + ( b - 18 ) = 0.x + 0

comparing LHS and RHS we will get

9 - a = 0

$\boxed{ \tt \: a = 9}$

and

b - 18 = 0

$\boxed{\tt \: b = 18}$

Hence, the value of a will be 9

and b will be 18.