How do I substitute coefficients into the quadratic formula?

Conditions

• The equation is in standard form $ax^2 + bx + c = 0$.
• The coefficients $a$, $b$, and $c$ have been correctly identified.

Reasoning, step by step

1. Write down the quadratic formula.
2. Identify the values of $a$, $b$, and $c$.
3. Substitute $-b$ with the negative of the $x$ coefficient.
4. Substitute $b^2$ with the square of the $x$ coefficient.
5. Substitute $4ac$ with four times the product of the $x^2$ coefficient and the constant term.
6. Substitute $2a$ with twice the $x^2$ coefficient.
7. Ensure negative values are enclosed in parentheses.

Example

For $6x^2 - 17x + 12 = 0$, $a=6$, $b=-17$, $c=12$. Substituting gives $x = \frac{-(-17) \pm \sqrt{(-17)^2 - 4(6)(12)}}{2(6)}$.

Common misconceptions

• Omitting parentheses around negative coefficients, leading to sign errors in the discriminant.
• Confusing the positions of $a$, $b$, and $c$ in the formula.

Watch the explanation

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