Find the value of $k + 3$ , if $(x - 2)$ is a factor of $2 x^{3} - 6 x^{2} + 5 x + k = 0$

Open in App

Solution

Let $f (x) = 2 x^{3} - 6 x^{2} + 5 x + k$
$g (x) = x - 2$
$x - 2 = 0$
$x = 2$
If $g (x)$ is a factor of $f (x)$ , then $f (2)$ must be equal to zero.
$∴ f (2) = 0$
$=> 2 (2)^{3} - 6 (2)^{2} + 5 (2) + k = 0$
$=> 16 - 24 + 10 + k = 0$
$=> k + 2 = 0$
$=> k = - 2$

Suggest Corrections

Similar questions

Find the value of 'a' if (x-2) is factor of 2x³− 6x²+ 5x + a.

-

-

(2 x - 3)

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

k

k

6 x^{2} - x - k = 0

\frac{3}{2}

(x + 2)

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

Join BYJU'S Learning Program