In the quadratic formula, x=−b±b2−4ac√2a𝑥=−𝑏±𝑏2−4𝑎𝑐2𝑎, the discriminant is the value of which portion of the formula?Question 1Select one:2a2𝑎b2−4ac𝑏2−4𝑎𝑐−b−𝑏x

Break Down the Problem

1. Identify the components of the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
2. Understand what the discriminant is in the context of a quadratic equation.

Relevant Concepts

3. The discriminant is defined as the expression under the square root in the quadratic formula, which is used to determine the nature of the roots of the quadratic equation ax² + bx + c = 0.

Analysis and Detail

4. In the formula $b^2 - 4ac$:
   • If $b^2 - 4ac > 0$, there are two distinct real roots.
   • If $b^2 - 4ac = 0$, there is exactly one real root (a repeated root).
   • If $b^2 - 4ac < 0$, there are no real roots (the roots are complex).

Verify and Summarize

5. In summary, the discriminant is the value of the expression $b^2 - 4ac$ in the quadratic formula.

Final Answer

The discriminant in the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ is given by $b^2 - 4ac$.