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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
Solution
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.
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