In the quadratic equation x² + 12x + c = 0, for the equation to have exactly one solution, the discriminant should be zero. Substituting the given values into the discriminant (b² - 4ac = 0) and solving for 'c', we find that when c = 36, the equation will have exactly one solution.
The equation x² + 12x + c = 0 is a quadratic equation, and usually a quadratic equation has two solutions. The formula for finding the solutions is given by -b ± √(b² - 4ac) / 2a. In this equation, 'a' is 1, and 'b' is 12.
For the equation to have exactly one solution, the term under the square root in the quadratic formula, called the discriminant (b² - 4ac), must be zero because the square root of zero is zero. This results in -b ± 0, effectively leading to a single solution.
So, in order to have only one solution: b² - 4ac = 0. Substituting the given values we get: (12)² - 4(1)c = 0 i.e., 144 - 4c = 0. Solving for c, we get c = 36. Therefore, for c = 36, the equation x² + 12x + c = 0 has exactly one solution.
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Answer:
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Step-by-step explanation:
A: 42
B: 61.2
C: 80.5
D: 118.9
Answer:
x= 3
Step-by-step explanation:
5x-2=13 - Add 2 to both sides which cancels out the -2 and turns 13 into 15
5x=15 - Divide 5 on both sides which cancels the 5 and leaves x=3
x=3 - Is the final answer or the solution to the problem