Determine the Set of Values of k for Which the Equation Has Real Roots
Solution
Given: $$2x^2-5x-k=0$$
Here, $$a=2,\quad b=-5,\quad c=-k$$
For real roots, $$D=b^2-4ac\ge0$$
$$(-5)^2-4(2)(-k)\ge0$$
$$25+8k\ge0$$
$$k\ge-\frac{25}{8}$$
Answer
The quadratic equation has real roots when $$\boxed{k\ge-\frac{25}{8}}$$