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.