Explain what value or values of c make the equation x^2+12x+c=0 have 1 and only one solution (please justify the answer) Thanks so much!!

Answers

Answer 1
Answer: only one solution means thtat it factors to a perfect square

to do that, we do
the number in front of the x^2 is 1
then take 1/2 of the number in front of the x term and square it and that is the constant term
12/2=6 6^2=36

36=c

x^2+12x+36=0
(x+6)^2=0
x+6=0
x=-6
Answer 2
Answer:

Final answer:

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.

Explanation:

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.

Learn more about Quadratic Eqations here:

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Please help I need it today (show solving steps please)​

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Answer:

but, i need the help....

Step-by-step explanation:

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Answers

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Total of 4 friends.
1200/4=300
Remove the zeroes and add them back at the end
12/4=3
300

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A: 42
B: 61.2
C: 80.5
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Answers

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Answers

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What is the solution to 5x−2=13 ? Plot the solution on the number line.

Answers

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