Question

After being rearranged and simplified, which of the following equations could be solved using the quadratic formula?

Check all that apply.

A. 2x2 - 3x + 10 = 2x + 21
B. 2x2 - 6x - 7 = 2x2
C. 5x2 + 2x - 4 = 2x2
D. 5x3 - 3x + 10 = 2x2

Answer 1

A. 2x^2 - 3x + 10 = 2x + 21
2x^2 - 3x - 2x + 10 - 21 = 0
2x^2 - 5x - 11 = 0                              (quadratic equation)

2x^2 - 6x - 7 = 2x^2
2x^2 - 2x^2 - 6x - 7 = 0
-6x - 7 = 0                                          (not a quadratic equation)

5x^2 + 2x - 4 = 2x^2
5x^2 - 2x^2 + 2x - 4 = 0
3x^2 + 2x - 4                                      (quadratic equation)

5x^3 - 3x + 10 = 2x^2
5x^3 - 2x^2 - 3x + 10 = 0                    (not a quadratic equation)

Therefore, options a and c can be solved using the quadratic formula.