Determine whether the values −1 and 7/3 are solutions to the quadratic equation 3x2−4x−4=3.
To determine whether a value is a solution to a quadratic equation, we substitute the value into the equation and see if it satisfies it.
Let's substitute -1 into the equation:
3(-1)^2 - 4(-1) - 4 = 3
3(1) + 4 - 4 = 3
3 + 0 = 3
3 = 3
Since -1 satisfies the equation, it is a solution.
Now let's 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
Since 7/3 also satisfies the equation, it is also a solution.
Therefore, both -1 and 7/3 are solutions to the quadratic equation 3x^2 - 4x - 4 = 3.
To determine if -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.
Let's start with -1:
Replace x with -1 in the equation:
3(-1)^2 - 4(-1) - 4 = 3
Simplifying this equation gives us:
3 + 4 - 4 = 3
3 = 3
Since the equation is true when x = -1, -1 is a solution to the quadratic equation.
Now, let's try 7/3:
Replace x with 7/3 in the equation:
3(7/3)^2 - 4(7/3) - 4 = 3
Simplifying this equation gives us:
3(49/9) - 28/3 - 4 = 3
(49/3) - (28/3) - 4 = 3
(21/3) - (12/3) - 4 = 3
7 - 4 - 4 = 3
3 = 3
Since the equation is true when x = 7/3, 7/3 is also a solution to the quadratic equation.
Therefore, both -1 and 7/3 are solutions to the 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 can substitute each value into the equation and see if it holds true.
For -1:
Replace x with -1 in the equation: 3(-1)^2 - 4(-1) - 4 = 3
Simplifying: 3(1) + 4 - 4 = 3
This becomes: 3 + 4 - 4 = 3
Simplifying further: 3 = 3
Since both sides of the equation are equal, -1 is a solution to the quadratic equation 3x^2-4x-4=3.
For 7/3:
Replace x with 7/3 in the equation: 3(7/3)^2 - 4(7/3) - 4 = 3
Simplifying: 3(49/9) - 28/3 - 4 = 3
This becomes: 49/3 - 28/3 - 4 = 3
Simplifying further: 21/3 - 4 = 3
Simplifying again: 7 - 4 = 3
Since both sides of the equation are not equal, 7/3 is not a solution to the quadratic equation 3x^2-4x-4=3.
In summary:
-1 is a solution to the quadratic equation 3x^2-4x-4=3,
while 7/3 is not a solution.