If f(a) = a^2 + a+ 1 , then number of solutions of equation f(a^2) = 3f(a) is

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1.Relation and Function

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If $f(a) = a^2 + a+ 1$ , then number of solutions of equation $f(a^2) = 3f(a)$ is

A

$0$

B

$1$

C

$2$

D

more than $2$

Solution

$f\left(a^{2}\right)-3 f(a)=0$

$\Rightarrow\left(a^{4}+a^{2}+1\right)-3\left(a^{2}+a+1\right)=0$

$\Rightarrow\left(a^{2}+a+1\right)\left(a^{2}-a+1\right)-3\left(a^{2}+a+1\right)=0$

$\Rightarrow\left(a^{2}+a+1\right)\left(a^{2}-a-2\right)=0$

Standard 12

Mathematics

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