For a quadratic equation in standard form $a{x}^2+bx+c=0$, what expression gives the discriminant?

• A. $4ac-b^2$
• B. $b^2+4ac$
• C. $b^2-4ac$
• D. $a^2-4bc$

Answer: (C)

Verified step by step guidance

1. 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 \(a \neq 0\).
2. 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.
3. The formula for the discriminant is \(\Delta = b^{2} - 4 a c\).
4. 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.
5. Therefore, the discriminant is given by the expression \(b^{2} - 4 a c\).