# Find k so that X^{2}+2x+k is a factor of 2x^{4}+x^{3}-14x^{2}+5x+6.Also find the zeroes of the two polynomials.

^{2}+2x+k is a factor of 2x

^{4}+x

^{3}-14x

^{2}+5x+6.Also find the zeroes of the two polynomials.

### Asked by bosesreyan | 2nd May, 2015, 09:18: PM

Expert Answer:

### Use long division method for the given polynomials as shown below:
We get the remainder as .
Since, is a factor of the given polynomial, the remainder should be zero.
Hence,
21+7k=0 and 2k^{2}+8k+6=0 at the same time.
k= -3 satisfies both equations. Hence, k=-3.
So we can write the polynomial as
Hence, the zeroes of are
The above two are factors of the 4th degree polynomial as well.
The other two roots of the 4th degree polynomial are roots of the quadratic

^{2}+8k+6=0 at the same time.

### Answered by satyajit samal | 4th May, 2015, 12:50: PM

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