Question

Find the values of a and b, if x² − 4 is a factor of ax⁴ + 2x³ − 3x² + bx − 4

Answer 1

Let and be the given polynomial.

We have,

are the factors of g(x).

By factor theorem, if and both are the factor of f(x)

Then f(2) and f(−2) are equal to zero.

Therefore,

and

Adding these two equations, we get

Putting the value of a in equation (i), we get

Hence, the value of a and b are 1, − 8 respectively.