Question 364165
The solution(s) to a quadratic equation is(are) x = 9.
Yes, a quadratic equation may have a "single" solution, but this is known as a "double" solution.
To write the equation whose solution(s) is(are) x = 9, you will start by setting x = 9.
To get such a solution you must have found the factors of the quadratic equation to be:
{{{x-9 = 0}}} and {{{x-9 = 0}}} Now if you multiply these factors together, the result will be the generating quadratic equation:
{{{(x-9)(x-9) = x^2-18x+81}}}
So the equation is:
{{{highlight(y = x^2-18x+81)}}}
Here's the graph of this quadratic equation and you can see why there appears to be a "single" solution:
{{{graph(400,400,-5,20,-5,100,x^2-18x+81)}}}