Find the solutions to the quadratic equation 2x² + 5x − 12 = 0.

1. x = 3 2 and x = -4
2. x = - 3 2 and x = 4
3. x = - 3 2 and x = -4
4. x = 3 2 and x = 4

A.
Correct! The solutions to the equation are 3/2 and -4.

B.
Incorrect. Remember, after you factor set each factor equal to 0 and then solve each equation.

C.
Incorrect. Remember, after you factor set each factor equal to 0 and then solve each equation.

D.
Incorrect. Remember, after you factor set each factor equal to 0 and then solve each equation.

Find the solutions to the quadratic equation 2x² + x = 15.

A. x = 2.5 and x = 3
Incorrect. Remember, after you factor set each factor equal to 0 and then solve each equation.

B. x = 2.5 and x = -3
Correct! The solutions to the equation are 2.5 and -3.

C. x = -2.5 and x = 3
Incorrect. Remember, after you factor set each factor equal to 0 and then solve each equation.

D. x = -2.5 and x = -3
Incorrect. Remember, after you factor set each factor equal to 0 and then solve each equation.

Which of the following best represents the solutions to the quadratic equation 5n² − 10n + 4 = 0?

A. n ≈ -0.6 and n ≈ -1.4
Incorrect. Remember to use –b in the quadratic formula.

B. n ≈ -0.6 and n ≈ 1.4
Incorrect. Remember to use –b in the quadratic formula.

C. n ≈ 0.6 and n ≈ -1.4
Incorrect. Remember to use –b in the quadratic formula.

D. n ≈ 0.6 and n ≈ 1.4
Correct! The solutions are approximately 0.6 and 1.4.

After completing the square, which quadratic equation is equivalent to x² − 4x + 2 = 0?

A. (x − 2)² = -2
Incorrect. Remember to add 4 to the right side of the equation.

B. (x − 4)² = 14
Incorrect. Remember to take 1/2 of the middle term before squaring.

C. (x − 2)² = 2
Correct! After moving the constant 2 to the right side of the equation where it would become -2, add 4 to both sides in order to complete the square.

D. (x − 2)² = -6
Incorrect. -2 squared equals 4.

Jonah has been asked to solve 2x² + 4x = 5 using the quadratic formula. What would be the values of a, b, and c?

A. a = 2, b = 4, and c = 5
Incorrect. The value of c will become negative when the equation is set equal to 0.

B. a = 2, b = 4, and c = -5
Correct! The values for a = 2, b = 4, and c = –5.

C. a = 2, b = -4, and c = -5
Incorrect. The value of b will remain positive.

D. a = 2, b = -4, and c = 5
Incorrect. The value of b is positive and the value of c will become negative when the equation is set equal to 0.