find k so that x2+2x+k is a factor of 2x4+x3-14x2+5x+6.also,find all zeroes of the polynomial.
Asked by FEHMEEDAH NAZNEEN | 31st Aug, 2010, 09:34: AM
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 2k2+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
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.
is a factor of the given polynomial, the remainder should be zero.Hence,
21+7k=0 and 2k2+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
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
Answered by | 5th May, 2015, 12:04: PM
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