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If x^(2)+2x-5 is a factor of x^(4)-2x^(3...

If `x^(2)+2x-5` is a factor of `x^(4)-2x^(3)+px^(2) +qx-35`, then find the value of `p^(2)-q`.

Text Solution

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Since `x^(2)+2x-5` is a factor of `x^(4)-2x^(3)+px^(2)+qx-35`, therefore on actual division, we must have the remainder 0.

Since, remainder will be zero,
`therefore` coefficient of x will be zero and constant =0
i.e., -46-2p+q=0 and `30+5p=0 implies p=-6`
`therefore -46-2(-6)+q=0 implies q=46-12=34`
`therefore p^(2)-q=(-6)^(2)-34`
=36-34=2
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