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