Question

find the value of k if x minus 2 is a factor of 4 x cube + 3 x square - 4 x + k ​

Answer 1

Answer:

k = - 36

Step-by-step explanation:

$4 {x}^{3} + 3 {x}^{2} - 4x + k = 0 \\ x - 2 = 0 \\ x = 2 \\ therefore \: substitute \: 2 \: in \: the \: equation \\ 4 \times {(2)}^{3} + 3 \times {(2)}^{2} - 4 \times 2 + k = 0 \\ \\ 4 \times 8 + 3 \times 4 - 4 \times 2 + k = 0 \\ 32 + 12 - 8 + k = 0 \\ 44 - 8 + k = 0 \\ 36 + k = 0 \\ k = - 36$

Answer 2

The value of k is -36

Solution:

Given that,

$4x^3 + 3x^2 - 4x + k$

Let,

$f(x) = 4x^3 + 3x^2 - 4x + k$

Also,

x - 2 is a factor

By factor theorem,

x - k is a factor of the polynomial f(x) if and only if f(k) = 0

Therefore,

x - 2 = 0

x = 2

Substitute x = 2 in given,

$f(x) = 0$

$4x^3 + 3x^2 - 4x + k = 0\\\\4(2)^3 + 3(2)^2 - 4(2) + k = 0\\\\4 \times 8 + 3 \times 4 - 8 + k = 0\\\\32 + 12-8 + k = 0\\\\32 + 4 + k = 0\\\\k + 36 = 0\\\\k = -36$

Thus the value of k is -36

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