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# In the Following Determine the Set of Values of K for Which the Given Quadratic Equation Has Real Roots: - Mathematics

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#### Question

In the following determine the set of values of k for which the given quadratic equation has real roots: $2 x^2 + x + k = 0$

#### Solution

The given quadric equation is $2 x^2 + x + k = 0$,and roots are real.

Then find the value of k.

Here,

$a = 2, b = 1, c = k$

As we know that D = b^2 - 4ac

Putting the value of

$a = 2, b = 1, c = k$

$D = 1 - 8k$
The given equation will have real roots, if D≥0

$D = 1 - 8k \geq 0$

$\Rightarrow 8k \leq 1$

$\Rightarrow k \leq \frac{1}{8}$

Therefore, the value of $k \leq \frac{1}{8}$.

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