Question

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)

• A. If $a=1$, then the equation has exactly one root is infinite.
• B. If $a=3$, then the equation is satisfied by more than 2 distinct real values of $x$.
• C. If $a=-2$, then the equation has both the roots are infinite.
• D. If $a=5$, then the equation has exactly one root is zero.

Answer 1

Answer: (B), (D)

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 $x\ne 0\therefore$ equation has exactly one root is infinite.
for $a=5,$ constant term is zero and equation has exactly one root is zero