Question

Find integral values of $k$ for which quadratic equation $\left(k-12\right)x^2+2\left(k-12\right)x+2=0$ posses no real roots?

Answer 1

$(k-12)x^2+2(k-12)x+2=0$ should not have real rats

$\Rightarrow b^2<4ac$

$\Rightarrow \left[2\right(k-12){]}^2<4(k-12\left)\right(2)$

$\Rightarrow A(k-12)(k-12)<(k-12)\left(2\right)$

$\Rightarrow (k-12)[k-12-2]<0$

$\Rightarrow (k-12)(k-14)<0$

$\Rightarrow k\in (12,14)$

But $k$ should be integral value.

$\Rightarrow k=13$