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