Find the values of a and b, if `x^2-4` is a factor of `ax^4+2x^3-3x^2+bx-4.`

Explanation

If `x^2−4` is a factor of `ax^4+2x^33x^2+bx−4x^2−4=0x=±2` are zeroes of the polynomial `p(x)=ax^4+2x^3−3x^2+bx−4`
`∴p(2)=0` and `p(−2)=0`
>`p(2)=0`
Then
`16a+16−12+2b−4=0`
`16a+2b=0`.......(1)
`p(−2)=0`
Then,
`16a−16−12−2b−4=0`
`16a−2b=32`......(2)
Substract (2) from (1)we get:
`4b=−32`
`b=−8`
Substitute `b` in equation (1) we get
`16a−16=0`
` :.a=1` and `b=−8`