Question

If the equation $a(x-1{)}^2+b\left(x^2-3x+2\right)+x-a^2=0$ is satisfied for all $x\in R$ then the number of ordered pairs of $(a,b)$ can be

• A. 0
• B. 1
• C. 2
• D. infinite

Answer 1

Answer: (B)

Equation is an identity $\Rightarrow$ coefficient of $x^2=0=$ coefficient of $x=$ constant term
$\therefore a+b=0$ ......(1)
$-2a-3b+1=0$ ....(2) and $a+2b-a^2=0$....(3)
from (1) and (2) $a=-1$ and $b=1$
which also satisfies $(3)\Rightarrow (a,b)=(-1,1)\Rightarrow (B)$