Question

6. Find k so that x2 + 2x + k is a factor of 2x4 + x3 - 14x2 + 5x + 6. Also find all the zeroes
of the two polynomials.
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Answer 1

Step-by-step explanation:

let the value of k be 1

$x ^{2} + 2x + 1 \\ x ^{2} + (1 + 1)x + 1 \\ x ^{2} + 1x + 1x \\ x(x + ) + (x + 1) \\ (x + 1)(x + 1) \\ x = - 1$

putting the value of x in eq..

$2( - 1) ^{4} + ( - 1) ^{3} - 14( - 1) ^{2} + 5( - 1) + 6 \\ 2 - 3 - 14 - 5 + 6 \\ 8 - 22 \\ = - 14 \\ solving \: for \: k \\ ( - 1) {}^{2} + 2( - 1) + k \\ 1 - 2 + k = 0 \\ - 1 + k = 0 \\ k = 1$