Question

What types of solutions will a quadratic equation have when the discriminant b2 − 4ac in the quadratic formula is a perfect square?

Answer 1

The discriminant must be zero.

Step-by-step explanation:

A Perfect-Square Trinomial is given by the form:

$(\alpha x \pm \beta)^2=(\alpha^2x^2 \pm 2\alpha x \beta + \beta^2)$

The discriminant in the quadratic formula is:

$\Delta=b^2-4ac \\ \\ \\ Here: \\ \\ a= \alpha^2 \\ \\ b=2\alpha \beta \\ \\ c=\beta^2 \\ \\ \\ So: \\ \\ \Delta=(2\alpha \beta )^2-4(\alpha^2)(\beta^2) \\ \\ \Delta=4\alpha^2 \beta^2-4\alpha^2 \beta^2=0$

So in order to get a perfect square, the discriminant must be zero.

Learn more:

Discriminant: https://brainly.com/question/1537997

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