First slide

Theory of equations

Question

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

Moderate

A

4
B

5
C

6
D

7

Solution

Roots are non real if discriminant $< 0$
i.e. if $5^{2} - 4.1 k < 0 i . e . if 4 k > 25 i . e . if k > \frac{25}{4}$
Hence, the required least integer k is 7.

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