Determine the Set of Values of k for Which the Equation Has Real Roots
Solution
Given: $$3x^2+2x+k=0$$
Here, $$a=3,\quad b=2,\quad c=k$$
For real roots, $$D=b^2-4ac\ge0$$
$$2^2-4(3)(k)\ge0$$
$$4-12k\ge0$$
$$k\le\frac{1}{3}$$
Answer
The quadratic equation has real roots when $$\boxed{k\le\frac{1}{3}}$$