1.

Find K, so that x^(2)+2x+K is a factor of 2x^(4)+x^(3)-14x^(2)+5x+6 . Also find all the zeros of the two polynomials.

Answer»


Answer :On dividing `2X^(4)+X^(3)-14x^(2)+5x+6` by`x^(2)+2x+k`
We get `(7k+21)x+2k^(2)+8k+6` as remainder is zero.
`=> 7k+21=0` and `2k^(2)+8k+6=0`
`=> k=-3` and `k=-1` or `-3`
`=>k=-3`
Zeros of `x^(2)+2x-3` are `1`, `-3` and `2x^(4)+x^(3)-14x^(2)+5x+6` are `1`, `-3`, `2`, `-(1)/(2)`


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