Determine which of the following polynomial has

Question:

Determine which of the following polynomial has $x-2$ a factor

(i) $3 x^{2}+6 x-24$

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

Solution:

Let $p(x)=x^{5}-4 a^{2} x^{3}+2 x+2 a+3$

Since, $x+2 a$ is a factor of $p(x)$, then put $p(-2 a)=0$

$\therefore \quad(-2 a)^{5}-4 a^{2}(-2 a)^{3}+2(-2 a)+2 a+3=0$

$\Rightarrow \quad-32 a^{5}+32 a^{5}-4 a+2 a+3=0$

$\Rightarrow \quad-2 a+3=0$

$\Rightarrow \quad 2 a=3$

$\therefore$       $a=\frac{3}{2}$

Hence, the value of $a$ is $\frac{3}{2}$.

 

Leave a comment

Close

Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now