Can you show me an example of using the quadratic formula with negative coefficients?

Conditions

• The quadratic equation has at least one negative coefficient.
• The equation is in standard form $ax^2 + bx + c = 0$.

Reasoning, step by step

1. Identify the coefficients $a$, $b$, and $c$, paying attention to their signs.
2. Substitute the coefficients into the quadratic formula.
3. Simplify the double negative $-(-17)$ to $17$.
4. Calculate the square of the negative coefficient $(-17)^2 = 289$.
5. Compute the product $4ac = 4(6)(12) = 288$.
6. Subtract to find the discriminant: $289 - 288 = 1$.
7. Evaluate the square root and split the $\pm$ expression.

Example

The video solves $6x^2 - 17x + 12 = 0$ by identifying $a=6$, $b=-17$, $c=12$. It substitutes these to get $x = \frac{17 \pm \sqrt{289 - 288}}{12}$, which simplifies to $x = \frac{17 \pm 1}{12}$.

Common misconceptions

• Incorrectly calculating $(-17)^2$ as $-289$ instead of $289$.
• Forgetting that $-(-17)$ becomes positive $17$ in the numerator.

Watch the explanation

Explore next

• How do you solve a quadratic equation using the quadratic formula?
• What is the process for simplifying fractions like $18/12$ or $16/12$?