Determine the Set of Values of k for Which the Equation Has Real Roots
Solution
Given: $$2x^2+3x+k=0$$
Here, $$a=2,\quad b=3,\quad c=k$$
For real roots, $$D=b^2-4ac \ge 0$$
$$3^2-4(2)(k)\ge0$$
$$9-8k\ge0$$
$$k\le\frac{9}{8}$$
Answer
The quadratic equation has real roots when $$\boxed{k\le\frac{9}{8}}$$