Question

If $f:R\to R$ is defined by $f\left(x\right)=x^2-3x+2$, and $f(x^2-3x-2)=a{x}^4+b{x}^3+c{x}^2+dx+e$ $a+b+c+d+e=$

• A. $1$
• B. $2$
• C. $30$
• D. $20$

Answer 1

The correct option is B $2$

$\begin{array}{c}f\left(x\right)=x^2-3x+2\\ f(x^2-3x+2)=(x^2-3x+2{)}^2-3(x^2-3x+2)+2\\ f(x^2-3x+2)=x^2+9x^2+4-6x^3-12x+4x^2-3x^2+9x-6+2\\ \Rightarrow f(x^2-3x+2)=x^4-6x^3+10x^2-3x+0\\ Compearingwitha{x}^4+b{x}^3+c{x}^2+dx+e\\ \Rightarrow \therefore a=1,b=-6,c=10,d=-3ande=0\\ Hencea+b+c+d+e=1-6+10-3+0=2\end{array}$