How to find the value of the discriminant?

Understand the Problem

The question is asking how to calculate the value of the discriminant in a quadratic equation, which is typically represented as b² - 4ac where a, b, and c are coefficients from the equation ax² + bx + c = 0.

Answer

The value of the discriminant is computed using the formula $D = b^2 - 4ac$.
Answer for screen readers

The final answer will be the calculated value of the discriminant $D$ from the values substituted into the equation.

Steps to Solve

  1. Identify coefficients of the quadratic equation

First, determine the values of $a$, $b$, and $c$ from the quadratic equation in standard form, which is $ax^2 + bx + c = 0$.

  1. Substitute the coefficients into the discriminant formula

Use the formula for the discriminant, which is $D = b^2 - 4ac$. Substitute the identified values of $a$, $b$, and $c$ into this formula.

  1. Calculate the discriminant

Perform the calculations based on the substituted values. Make sure to first square the value of $b$ and then multiply $a$ and $c$ by 4 before subtracting.

  1. Write the final equation and compute

Write out the complete equation for the discriminant and compute the result.

$$ D = b^2 - 4ac $$

The final answer will be the calculated value of the discriminant $D$ from the values substituted into the equation.

More Information

The discriminant helps to determine the nature of the roots of the quadratic equation. If $D > 0$, there are two distinct real roots; if $D = 0$, there is exactly one real root; and if $D < 0$, there are two complex roots.

Tips

  • Misidentifying the coefficients: Always double-check the values of $a$, $b$, and $c$ from the equation.
  • Incorrectly applying the formula: Ensure that you follow the order of operations (PEMDAS/BODMAS) when computing the discriminant.

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