# The least value of k which makes the roots of the equation x

Question:

The least value of $k$ which makes the roots of the equation $x^{2}+5 x+k=0$ imaginary is

(a) 4

(b) 5

(c) 6

(d) 7

Solution:

(d) 7

The roots of the quadratic equation $x^{2}+5 x+k=0$ will be imaginary if its discriminant is less than zero.

$\therefore 25-4 k<0$

$\Rightarrow k>\frac{25}{4}$

Thus, the minimum integral value of k for which the roots are imaginary is 7.