Question

value of a if x+a is a factor of x^2-4ax+5a^2​

Answer 1

Answer:

The answer is $a=0$

Step-by-step explanation:

• Factor theorem : If $x-a$ is a factor of a polynomial P(x), then $P(a)=0$

           Here given $x+a=x-(-a)$ is a factor of $P(x)=x^2-4ax+5a^2$

                                   $\Rightarrow P(-a)=0\\\Rightarrow (-a)^2-4a(-a)+5a^2=0\\\Rightarrow a^2+4a^2+5a^2=0\\\Rightarrow 10a^2=0\\\Rightarrow a^2=\frac{0}{10}=0\\\Rightarrow a=0$