Question

Find k if x = 2 p(x) = 2x⁴ + 9x³ + kx² + 4x - 6​

Answer 1

SOLUTION

GIVEN

x = 2 is a zero of the polynomial

p(x) = 2x⁴ + 9x³ + kx² + 4x - 6

TO DETERMINE

The value of k

EVALUATION

Here the given polynomial is

p(x) = 2x⁴ + 9x³ + kx² + 4x - 6

Now x = 2 is a zero of the polynomial

∴ p(2) = 0

$\sf{ \implies \: 2 \times {(2)}^{4} + 9 \times {(2)}^{3} + k \times {(2)}^{2} + 4 \times 2 - 6 = 0 }$

$\sf{ \implies \: 32 + 72 + 4k + 8 - 6 = 0 }$

$\sf{ \implies \: 32 + 72 + 4k + 2 = 0 }$

$\sf{ \implies \: 4k + 106= 0 }$

$\sf{ \implies \: 4k = - 106}$

$\sf{ \implies \: k = - 26.5}$

FINAL ANSWER

Hence the required value of k = - 26.5

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