Question

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

Answer 1

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

Then find the value of k.

Here,

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

As we know that ${\displaystyle D=b^2-4ac}$

Putting the value of

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

$$D=1-8k$$

The given equation will have real roots, if D≥0

$$D=1-8k\ge 0$$

$$\Rightarrow 8k\le 1$$

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

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