Find ' k ' so that ( x2+2x+k ) is a factor of ( 2x4 + x3 - 14x2 + - Maths - Polynomials

Question

Find ' k ' so that ( x2+2x+k ) is a factor of (
2x4 + x3 - 14x2 + 5x + 6 ) Also
find all the zeroes of both the polynomials

Aakash Sharma · Accepted Answer

For $(x^{2} + 2 x + k)$ to be a factor of $(2 x^{4} + x^{3} - 14 x^{2} + 5 x + 6)$ on dividing it should leave remainder as zero So,

Comparing the coefficient of x we get $21 + 7 k = 0 \Rightarrow k = \frac{- 21}{7} = - 3 So the x^{2} + 2 x + k = x^{2} + 2 x - 3 = (x - 1) (x + 3)$ Thus its zeroes are 1, â€“3 and $2 x^{4} + x^{3} - 14 x^{2} + 5 x + 6 = (x^{2} + 2 x + k) (2 x^{2} - 3 x - 18 + 2 k) = (x^{2} + 2 x - 3) (2 x^{2} - 3 x - 2) = (x - 1) (x + 3) (x - 2) (2 x + 1) Hence its zeroes are 1, - 3, 2, \frac{- 1}{2}$

Find ' k ' so that ( x2+2x+k ) is a factor of ( 2x4 + x3 - 14x2 + 5x + 6 ). Also find all the zeroes of both the polynomials.

Find ' k ' so that ( x²+2x+k ) is a factor of ( 2x⁴ + x³ - 14x² + 5x + 6 ). Also find all the zeroes of both the polynomials.