Determine whether the values -1 and 7/3 are solutions to the quadratic equation 3x^2 - 4x - 4 = 3

Answer 1

To determine if a value is a solution to a quadratic equation, you need to substitute the value into the equation and check if the equation is true.

For the equation 3x^2 - 4x - 4 = 3,
Substituting x = -1:
3(-1)^2 - 4(-1) - 4 = 3
3 + 4 - 4 = 3
3 = 3

The equation is true when x = -1.

Substituting x = 7/3:
3(7/3)^2 - 4(7/3) - 4 = 3
3(49/9) - 28/3 - 36/3 = 3
147/9 - 64/3 - 108/9 = 3
147/9 - 192/9 - 108/9 = 3
(147 - 192 - 108)/9 = 3
-153/9 = 3
-17 = 3

The equation is not true when x = 7/3.

Therefore, the value -1 is a solution to the quadratic equation, but 7/3 is not.