To determine whether the values 3 and 4 are solutions to the quadratic equation x^2−7x+12=0, we can substitute each value into the equation and see if it satisfies the equation.
For x = 3:
3^2 - 7(3) + 12 = 9 - 21 + 12 = 0
Since the expression equals 0, x = 3 is a solution.
For x = 4:
4^2 - 7(4) + 12 = 16 - 28 + 12 = 0
Again, the expression equals 0, so x = 4 is also a solution.
Therefore, the correct answer is Option #3: Both x=3 and x=4 are solutions.
Determine 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 #
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For the quadratic equation x2+20x=69 , complete the table by testing each of the given values to determine whether it is a solution. Identify which one of these values is in the solution set. (1 point) Only x= is in the solution set.
To determine whether the given values are solutions to the quadratic equation x^2 + 20x = 69, we can substitute each value into the equation and see if it satisfies the equation.
For x = 0:
0^2 + 20(0) = 0 + 0 = 0, which is not equal to 69.
Therefore, x = 0 is not a solution to the equation.
For x = 1:
1^2 + 20(1) = 1 + 20 = 21, which is not equal to 69.
Therefore, x = 1 is not a solution to the equation.
For x = -1:
(-1)^2 + 20(-1) = 1 - 20 = -19, which is not equal to 69.
Therefore, x = -1 is not a solution to the equation.
For x = 2:
2^2 + 20(2) = 4 + 40 = 44, which is not equal to 69.
Therefore, x = 2 is not a solution to the equation.
For x = -2:
(-2)^2 + 20(-2) = 4 - 40 = -36, which is not equal to 69.
Therefore, x = -2 is not a solution to the equation.
For x = 3:
3^2 + 20(3) = 9 + 60 = 69, which is equal to 69.
Therefore, x = 3 is a solution to the equation.
From the given values, only x = 3 is in the solution set of the equation.
For x = 0:
0^2 + 20(0) = 0 + 0 = 0, which is not equal to 69.
Therefore, x = 0 is not a solution to the equation.
For x = 1:
1^2 + 20(1) = 1 + 20 = 21, which is not equal to 69.
Therefore, x = 1 is not a solution to the equation.
For x = -1:
(-1)^2 + 20(-1) = 1 - 20 = -19, which is not equal to 69.
Therefore, x = -1 is not a solution to the equation.
For x = 2:
2^2 + 20(2) = 4 + 40 = 44, which is not equal to 69.
Therefore, x = 2 is not a solution to the equation.
For x = -2:
(-2)^2 + 20(-2) = 4 - 40 = -36, which is not equal to 69.
Therefore, x = -2 is not a solution to the equation.
For x = 3:
3^2 + 20(3) = 9 + 60 = 69, which is equal to 69.
Therefore, x = 3 is a solution to the equation.
From the given values, only x = 3 is in the solution set of the equation.
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