The quadratic formula | AP Precalculus | Tope Teaches Maths

PrerequisitesPrerequisite

Substitute into the quadratic formula and give both solutions.

First write the equation as , then identify , and , including signs.
Use . The entire numerator is divided by .
Calculate once with the plus sign and once with the minus sign. Keep exact values unless rounding is requested.

Example 1

Two rational solutions

Solve using the quadratic formula.

,

,

Solve the other square-root branch as well, then collect all roots.

Evaluate the plus and minus branches and list all solutions.

Example 2

Leave a radical exact

Use the quadratic formula to find all real solutions.

,

,

Solve the other square-root branch as well, then collect all roots.

Remember
If , there are no real solutions. If it equals zero, the two roots coincide.

Your turn

Question 1

Solve using the quadratic formula. Give exact answers.

Check answer

Take both square roots. Include positive and negative roots.

Evaluate the plus and minus branches and list all solutions.

Question 2

Solve using the quadratic formula. Give exact answers.

Check answer

Take both square roots. Include positive and negative roots.

Evaluate the plus and minus branches and list all solutions.

Question 3

Solve using the quadratic formula. Give exact answers.

Check answer

Take both square roots. Include positive and negative roots.

Evaluate the plus and minus branches and list all solutions.

Question 4

Solve using the quadratic formula. Give exact answers.

Check answer

Take both square roots. Include positive and negative roots.

Solve the other square-root branch as well, then collect all roots.

Question 5

Solve using the quadratic formula. Give exact answers.

Check answer

Take both square roots. Include positive and negative roots.

Solve the other square-root branch as well, then collect all roots.

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