For what values of the real parameter does the quadratic equation have two distinct real roots?

Answer and explanation

Correct answer: B. or

Using the reduced discriminant :
.
.
The roots of the corresponding equation are and . Since the parabola opens upward, the expression is strictly positive outside the roots: or .
  1. Step 1: A quadratic equation has two distinct real roots if and only if its discriminant .
  2. Step 2: Factor the quadratic inequality :
Answer
or .

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