Determine whether the values −1 and 7/3 are solutions to the quadratic equation 3x^2−4x−4=3 .
To determine whether the values -1 and 7/3 are solutions to the quadratic equation 3x^2 - 4x - 4 = 3, we need to substitute these values into the equation and see if they satisfy it.
Step 1: Substitute -1 into the equation:
3(-1)^2 - 4(-1) - 4 = 3
3(1) + 4 - 4 = 3
3 + 4 - 4 = 3
3 = 3
The equation is satisfied when x = -1.
Step 2: Substitute 7/3 into the equation:
3(7/3)^2 - 4(7/3) - 4 = 3
3(49/9) - 28/3 - 4 = 3
147/9 - 28/3 - 4 = 3
(147 - 84 - 36)/9 = 3
(27/9) = 3
3 = 3
The equation is satisfied when x = 7/3.
Therefore, both -1 and 7/3 are solutions to the quadratic equation 3x^2 - 4x - 4 = 3.
To determine whether −1 and 7/3 are solutions to the quadratic equation 3x^2−4x−4=3, we substitute each value into the equation and see if it holds true.
For −1:
3(-1)^2 − 4(-1) − 4 = 3
3(1) + 4 - 4 = 3
3 + 4 - 4 = 3
3 = 3
The equation holds true for −1, so −1 is a solution.
For 7/3:
3(7/3)^2 − 4(7/3) − 4 = 3
3(49/9) - 28/3 - 4 = 3
147/9 - 28/3 - 12/3 = 3
147/9 - (28 + 12)/3 = 3
147/9 - 40/3 = 3
(147 - (40*3))/9 = 3
147 - 120 = 27
27 = 27
The equation holds true for 7/3, so 7/3 is also a solution.
Therefore, both −1 and 7/3 are solutions to the quadratic equation 3x^2−4x−4=3.
To determine whether the values −1 and 7/3 are solutions to the quadratic equation 3x^2−4x−4=3, we need to substitute these values into the equation and check if they satisfy it.
Let's start with -1:
Substituting x = -1 into the equation:
3(-1)^2 - 4(-1) - 4 = 3
3(1) + 4 - 4 = 3
3 + 4 - 4 = 3
7 - 4 = 3
3 = 3
Since the left side of the equation equals the right side, -1 is a solution to the quadratic equation.
Now let's move on to 7/3:
Substituting x = 7/3 into the equation:
3(7/3)^2 - 4(7/3) - 4 = 3
3(49/9) - 28/3 - 4 = 3
147/9 - 28/3 - 4 = 3
(147 - 84 - 36)/9 = 3
(27)/9 = 3
3 = 3
Again, the left side of the equation is equal to the right side, so 7/3 is also a solution to the quadratic equation.
Therefore, both −1 and 7/3 are solutions to the quadratic equation 3x^2−4x−4=3.