Question

The least value of k which makes the roots of the equation  \[x^2 + 5x + k = 0\]  imaginary is

Options

• 4

• 5

• 6

• 7

Answer 1

7

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

\[\therefore 25 - 4k < 0\]

\[ \Rightarrow k > \frac{25}{4}\]

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