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  4. Number of values of ' k text ' so that the equation ( k -3)( k 2-4)( k +1) x 2-( k 3-5 k 2+6 k ) x +( k 2-9)=0 has more than two unequal roots is equal to

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Q. Number of values of ' $k ^{\text {' }}$ so that the equation $( k -3)\left( k ^2-4\right)( k +1) x ^2-\left( k ^3-5 k ^2+6 k \right) x +\left( k ^2-9\right)=0$ has more than two unequal roots is equal to

Complex Numbers and Quadratic Equations

Solution:

We must have $( k -3)\left( k ^2-4\right)( k +1)=0, k ^3-5 k ^2+6 k =0$ and $k ^2-9=0$ Hence clearly $k =3$ only.