Write a quadratic equation in the variable x having the given numbers as solutions. Type the equation in standard form ax^2+bx +c = 0
The solution is 6 only solution.
(x-6)(x-6) = 0
expand and simplify
Sure, here's a quadratic equation with 6 as the only solution:
x^2 - 12x + 36 = 0
Remember, though, it might not be as funny as a clown's nose, but it should still put a smile on your face.
If 6 is the only solution to the quadratic equation, then we can write it as:
(x - 6)(x - 6) = 0
Expanding the equation, we get:
x^2 - 12x + 36 = 0
Therefore, the quadratic equation in standard form with 6 as the only solution is:
x^2 - 12x + 36 = 0
To write a quadratic equation with 6 as the only solution, we can start by using the fact that the solutions of a quadratic equation are given by the roots of the equation, which means that if 6 is the only solution, then (x - 6) must be a factor of the quadratic equation.
So, to find the quadratic equation, we can take (x - 6) as one of the factors and multiply it by another linear factor. Since there is only one solution, the other factor must also be (x - 6). We can write this as:
(x - 6)(x - 6) = 0
Expanding this equation, we get:
x^2 - 6x - 6x + 36 = 0
Combining like terms, we have:
x^2 - 12x + 36 = 0
So, the quadratic equation in standard form ax^2 + bx + c = 0, where a = 1, b = -12, and c = 36, is:
x^2 - 12x + 36 = 0.