Question

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

Answer 1

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 \[k \leq \frac{1}{8}\].