Determine the Set of Values of k for Which the Equation Has Real Roots
Solution
Given: $$2x^2+x+k=0$$
Here, $$a=2,\quad b=1,\quad c=k$$
For real roots, $$D=b^2-4ac\ge0$$
$$1^2-4(2)(k)\ge0$$
$$1-8k\ge0$$
$$k\le\frac{1}{8}$$
Answer
The quadratic equation has real roots when $$\boxed{k\le\frac{1}{8}}$$