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 soluation is 8 and is the only solution.
actually, 8 is not the only solution. There are two solutions, and they both have the value 8.
(x-8)(x-8) = x^2 - 16x + 64 = 0
To write a quadratic equation with the given solution of x = 8, we can use the fact that if x = 8 is a solution, then (x - 8) must be a factor of the quadratic equation. This is because the roots of the equation are the values of x that make it equal to zero, so if x = 8 is a solution, then (x - 8) = 0.
Therefore, the quadratic equation with x = 8 as the only solution can be written as:
(x - 8)(a*x + b) = 0
Expanding this equation, we get:
ax^2 + bx - 8ax - 8b = 0
Rearranging the terms and combining like terms, we can write it in standard form as:
ax^2 + (b - 8a)x - 8b = 0
So, the quadratic equation in standard form with x = 8 as the only solution is ax^2 + (b - 8a)x - 8b = 0.