Textbook Question
Solve each equation in Exercises 41–60 by making an appropriate substitution.
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1. Equations & Inequalities
The Quadratic Formula
Multiple Choice
For a quadratic equation in standard form , what expression gives the discriminant?
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Verified step by step guidance1
Recall that the quadratic equation in standard form is given by \(a x^{2} + b x + c = 0\), where \(a\), \(b\), and \(c\) are constants and \(a \neq 0\).
The discriminant is a specific expression derived from the coefficients \(a\), \(b\), and \(c\) that helps determine the nature of the roots of the quadratic equation.
The formula for the discriminant is \(\Delta = b^{2} - 4 a c\).
This expression comes from the part under the square root in the quadratic formula \(x = \frac{-b \pm \sqrt{b^{2} - 4 a c}}{2a}\), which is used to find the roots of the quadratic equation.
Therefore, the discriminant is given by the expression \(b^{2} - 4 a c\).
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