Find the value of k for which the quadratic equation $2 x^{2} + 5 x + k = 0$ has no real roots.

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Solution

Consider the given equation.
$2 x^{2} + 5 x + k = 0$ $. . . . . . . (1)$

Since, the equation has no real roots.
$b^{2} - 4 a c < 0$

Therefore,
$5^{2} - 4 \times 2 \times k < 0$
$25 - 8 k < 0$
$25 < 8 k$
$k > \frac{25}{8}$

Hence, this is the answer.

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