Determine whether the values −1 and 7/3 are solutions to the quadratic equation 3x^2−4x−4=3
To determine if a given value is a solution to the quadratic equation, we substitute the value into the equation and see if the left side equals the right side.
First, let's substitute -1 into the equation:
3(-1)^2 - 4(-1) - 4 = 3
3 - (-4) - 4 = 3
3 + 4 - 4 = 3
3 = 3
Since the left side equals the right side, -1 is a solution to the quadratic equation.
Next, let's substitute 7/3 into the equation:
3(7/3)^2 - 4(7/3) - 4 = 3
3(49/9) - (28/3) - 4 = 3
(49/3) - (28/3) - 4 = 3
(49 - 28 - 12)/3 = 3
9/3 = 3
3 = 3
Again, the left side equals the right side, so 7/3 is a solution to the quadratic equation.
Therefore, both -1 and 7/3 are solutions to the quadratic equation 3x^2 - 4x - 4 = 3.