alleryStart learning →A quadratic with a perfect square solved by the quadratic formula gives how many solutions?
AExactly two solutions
BExactly three solutions
CNo solution at all
DJust one solution
Answer & Solution
Correct answer: D. Just one solution
1. A perfect square is the case where the two roots coincide.
2. The Zero Products Principle shows such an equation has only one solution.
3. The quadratic formula can solve the same equation.
4. Using the Quadratic Formula on an equation with a perfect square also gives just one solution.
5. That matches a discriminant of zero.
_Source: OpenStax Elementary Algebra 2e (CC BY 4.0), Ch 10 'Quadratic Equations', sections 10.1-10.5_
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