What is the role of the expression under the square root in the quadratic formula?

Conditions

• The quadratic formula is being applied.
• The coefficients $a$, $b$, and $c$ are known.

Reasoning, step by step

1. Identify the expression $b^2 - 4ac$ under the radical.
2. Substitute the coefficients $a$, $b$, and $c$ into this expression.
3. Calculate the squares and products.
4. Add or subtract the resulting numbers to find the value under the radical.
5. Evaluate the principal square root of this value.
6. Use this result in the numerator of the quadratic formula.

Example

In the example $2x^2 + 3x - 2 = 0$, the expression is $(3)^2 - 4(2)(-2)$. This calculates to $9 - (-16) = 25$. The square root of 25 is 5, which is then used in the formula as $\frac{-3 \pm 5}{4}$.

Common misconceptions

• Calculating $-4ac$ as $-4(2)(-2) = -16$ instead of $+16$, leading to an incorrect discriminant value.
• Assuming the expression under the square root is the final answer rather than an intermediate step.

Watch the explanation

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