Find the value of k for which (x -1) is a factor of $(2 x^{3} + 9 x^{2} + x + k)$ .

Open in App

Solution

ANSWER:
Let:
$f (x) = 2 x^{3} + 9 x^{2} + x + k$
x-1 is a factor of $f (x) = 2 x^{3} + 9 x^{2} + x + k$

.⇒ $f (1) = 0 \Rightarrow 2 \times 1^{3} + 9 \times 1^{2} + 1 + k = 0 \Rightarrow 12 + k = 0 \Rightarrow k = - 12$
Hence, the required value of k is -12.

Suggest Corrections

Similar questions

(2 x - 3)

2 x^{3} - 9 x^{2} + x + k

k

(x + 2)

2 x^{3} + 5 x^{2} - x - k

Find the value of $k$ if $(2 x - 3)$ is a factor of $2 x^{3} - 9 x^{2} + x + k .$

b

(2 x + 3)

2 x^{3} + 9 x^{2} - x - b .

Find the value of 'k' if 2x-3 is a factor of 2x3-ax2+x+k.

Join BYJU'S Learning Program