Question

The value of $a$ for which the equation $(a^2-3a+2)x^2+(a^2-5a+4)x+(a^2-1)=0$ has more than two roots is:

• A. $-1$
• B. $4$
• C. $2$
• D. $1$

Answer 1

The correct option is D $1$

If a quadratic equation in $x$ has more than two roots then it is identically zero at all values of $x$.
If a quadratic equation is identically zero then the co-efficients of $x^2$, $x$ and the constant term are identically zero.Equating the respective coefficient of $x^2,x$ and constant to $0$.
Hence, we get
$a^2-3a+2=0$
$(a-1)(a-2)=0$
$a=1$ and $a=2$
$a^2-5a+4=0$
$(a-4)(a-1)=0$
$a=1,4$
$a^2-1=0$
$a^2=1$
$a=\pm 1$
Taking the common, value of $a$, we get $a=1$.