Question

The least value of k which makes the roots of the equation $x^2+5x+k=0$ imaginary is
(a) 4
(b) 5
(c) 6
(d) 7

Answer 1

(d) 7

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

$$\begin{gathered} \therefore 25-4k<0 \\ \Rightarrow k>\frac{25}{4} \end{gathered}$$

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