In each of the following two polynomials, find the value of $a$ , if $x + a$ is a factor:

$x^{3} + a x^{2} - 2 x + a + 4$

Open in App

Solution

Given: $(x + a)$ is a factor of $x^{3} + a x^{2} - 2 x + a + 4$

Let $f (x) = x^{3} + a x^{2} - 2 x + a + 4$
$∵ (x + a)$ is a factor of $x^{3} + a x^{2} - 2 x + a + 4$

$∴ f (- a) = 0$ [Using factor theorem]

$\Rightarrow (- a)^{3} + a \times (- a)^{2} - 2 \times (- a) + a + 4 = 0$

$\Rightarrow - a^{3} + a^{3} + 2 a + a + 4 = 0$

$\Rightarrow 3 a + 4 = 0$

$\Rightarrow 3 a = - 4$

$∴ a = - \frac{4}{3}$

Hence, the value of $a = - \frac{4}{3}$

Suggest Corrections

Similar questions

In each of the following, two polynomials, find the value of a, if x + a is a factor.

(i) $x^{3} + a x^{2}$ - 2x + a + 4

(ii) $x^{4} - a^{2} x^{2}$ + 3x - a

x - 2

a

x^{5} - 3 x^{4} - a x^{3} + 3 a x^{2} + 2 a x + 4

a

x - a

x^{6} - a x^{5} + x^{4} - a x^{3} + 3 x - a + 2

Join BYJU'S Learning Program

Explore more

Join BYJU'S Learning Program