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  4. For quadratic equation ( k 2-3 k +2) x 2+4 x + k 2- k =0 sum of all values of k for which given equation has one root infinity.

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Q. For quadratic equation $\left( k ^2-3 k +2\right) x ^2+4 x + k ^2- k =0$ sum of all values of $k$ for which given equation has one root infinity.

Complex Numbers and Quadratic Equations

Solution:

$a =0, c \in R , b \neq 0 \text { (Already given) }$
$\Rightarrow \text { Exactly one root infinity } $
$a =0 \Rightarrow k =1,2 $
$\operatorname{sum}=1+2=3 $