What do you do when you have a plus-minus symbol in your final answer from the quadratic formula?

Q: What do you do when you have a plus-minus symbol in your final answer from the quadratic formula?

When the quadratic formula yields an expression with a $\pm$ symbol, you must split it into two separate calculations. One calculation uses the plus sign, and the other uses the minus sign, to find both roots of the quadratic equation.

When the quadratic formula yields an expression with a

\pm

symbol, you must split it into two separate calculations. One calculation uses the plus sign, and the other uses the minus sign, to find both roots of the quadratic equation.

Conditions

The expression contains a $\pm$ symbol representing two possible values.
You are solving a quadratic equation.

Reasoning, step by step

Identify the expression containing the $\pm$ symbol.
Write down the first equation using the $+$ sign.
Write down the second equation using the $-$ sign.
Evaluate the numerator for the first equation.
Evaluate the numerator for the second equation.
Simplify both resulting fractions to find the two distinct solutions.

Example

For the expression $x = \frac{17 \pm 1}{12}$ , the speaker splits it into $x = \frac{17 + 1}{12}$ and $x = \frac{17 - 1}{12}$ , which are then calculated as $\frac{18}{12}$ and $\frac{16}{12}$ .

Common misconceptions

Trying to combine the $+$ and $-$ signs into a single operation.
Forgetting to simplify the resulting fractions after splitting the $\pm$ expression.

Watch the explanation

YouTubeHow To Solve Quadratic Equations Using The Quadratic Formula

4:55 – 5:00Watch this moment ↗

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