Question

The integral value of $k$ for which the equation $(k-12)x^2+2(k-12)x+2=0$ possesses no real solutions is ______.

• A. 12
• B. 13
• C. 14
• D. All of the above

Answer 1

The correct option is B

13

We have $(k-12)x^2+2(k-12)x+2=0$
For no real solution, D < 0 i.e $b^2-4ac<0$
$\Rightarrow \left[2\right(k-12){]}^2-4(k-12)\times 2<0$
$\Rightarrow 2(k-12)\left[2\right(k-12)-4]<0$
$\Rightarrow (k-12)[2k-24-4]<0$
$\Rightarrow (k-12)(2k-28)<0$
$\Rightarrow 12<k<14\Rightarrow k=13$