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Q.
If the equation $a(x-1)^2+b\left(x^2-3 x+2\right)+x-a^2=0$ is satisfied for all $x \in R$ then the number of ordered pairs of $(a, b)$ can be
Complex Numbers and Quadratic Equations
Solution:
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+2 b-a^2=0$....(3)
from (1) and (2) $ a=-1$ and $b=1$
which also satisfies $(3) \Rightarrow (a, b)=(-1,1) \Rightarrow(B) $