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Q.
Let $(a-1)(a-3)(a+2) x^2-2(a-1)(a-3) x+(a-3)(a+2)(a-5)=0, a \in R$ be an equation, then identify the correct alternative(s)
Complex Numbers and Quadratic Equations
Solution:
for $a =1, $ coefficient of $x ^2 \&$ coefficient of $x$ both are zero but constant term is non-zero.
$\therefore$ equation has both roots infinite.
for $a =3, $ coefficient of $x ^2$, coefficient of $x$ and constant term all are zero equation becomes an identity
for $a=-2, $ coefficient of $x^2=0$ but coefficient of $x \neq 0 \therefore$ equation has exactly one root is infinite.
for $a=5, $ constant term is zero and equation has exactly one root is zero