Question

If x+a is a factor of 
${x}^{4} - {a}^{2} {x}^{2} + 3x + 3a$
then a=​

Answer 1

EXPLANATION:-

If x+a is a factor of the given polynomial then x=(-a) is  zero  of the polynomial .

Given polynomial:-

$\sf\p(x)=x^4-a^2x^2+3x+3a$

Since x=-a is a zero of the polynomial ,so P(-a)=0

Let's find the value of p(-a):-

$\sf\;p(a)=a^4-a^2(-a)^2+3(-a)+3(-a)\\\\p(x)=a^4-6a\\\\p(x)=-6a\\\\Since\;p(a)=0\\\\0=-6a\\\\a=0$

So the value of a is 0