etermine whether the values 3 and 4 are solutions to the quadratic equation x2−7x+12=0 , and then select the correct answer from the following options. Option #1: Only x=3 is a solution. Option #2: Only x=4 is a solution. Option #3: Both x=3 and x=4 are solutions. Option #4: Neither x=3 nor x=4 is a solution. (1 point) Option # Remaining Attempts : 3 Skip to navigation
To determine whether the values 3 and 4 are solutions to the given quadratic equation, we substitute these values into the equation and check whether the equation is satisfied.
For x = 3:
(3)^2 - 7(3) + 12 = 9 - 21 + 12 = 0
Since the equation is satisfied, x = 3 is a solution.
For x = 4:
(4)^2 - 7(4) + 12 = 16 - 28 + 12 = 0
Since the equation is satisfied, x = 4 is also a solution.
Therefore, both x = 3 and x = 4 are solutions to the quadratic equation.
The correct answer is Option #3: Both x = 3 and x = 4 are solutions.
To determine whether the values 3 and 4 are solutions to the quadratic equation x^2 - 7x + 12 = 0, we need to substitute these values into the equation and check if it holds true.
For x = 3:
Substituting x = 3 into the equation, we get:
(3)^2 - 7(3) + 12 = 9 - 21 + 12 = 0
Since the equation holds true, x = 3 is a solution.
For x = 4:
Substituting x = 4 into the equation, we get:
(4)^2 - 7(4) + 12 = 16 - 28 + 12 = 0
Again, the equation holds true, so x = 4 is also a solution.
Therefore, the correct answer is Option #3: Both x = 3 and x = 4 are solutions.
To determine whether the values 3 and 4 are solutions to the quadratic equation x^2 - 7x + 12 = 0, we can substitute these values into the equation and check if the equation holds true.
For x = 3:
Substituting x = 3 into the equation, we get:
(3)^2 - 7(3) + 12 = 0
9 - 21 + 12 = 0
0 = 0
Since the equation holds true when x = 3, x = 3 is a solution to the quadratic equation.
For x = 4:
Substituting x = 4 into the equation, we get:
(4)^2 - 7(4) + 12 = 0
16 - 28 + 12 = 0
0 = 0
Similarly, since the equation holds true when x = 4, x = 4 is also a solution to the quadratic equation.
Therefore, both x = 3 and x = 4 are solutions to the quadratic equation x^2 - 7x + 12 = 0.
The correct answer is Option #3: Both x = 3 and x = 4 are solutions.