Question

If both the roots of the quadratic equation $x^2-2kx+k^2+k-5=0$ are less then 5, then k lies in the Interval

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$x^2-2kx+k^2+k-5=0$

Roots are less than 5, D $\ge$ 0

$4k^2-4(k^2+k-5)\ge 0$ ........(i)

$\Rightarrow k\le 5\Rightarrow f\left(5\right)$ > 0 ........(ii)

$\Rightarrow kϵ(-\infty ,4)\cup (5,\infty );-\left(\frac{2k}{2}\right)$ < 5 $\Rightarrow$ k < 5 .........(iii)

From (i), (ii) and (iii), $kϵ(-\infty ,4)$