Problema Solution
Can you help answer this math question? Thank you.
How do you find a quadratic equation given only the solution? Is it possible to have different quadratic equations with the same solution? Explain why or why not.
Answer provided by our tutors
(1) If the solution is x =a and x = b, we could solve as follows:
x=a, so x-a=0
x=b, so x-b=0
(x-a)(x-b)=0
x^2 -(a+b)x + ab = 0
So we find a quadratic equation that x^2 -(a+b)x + ab = 0 which has the given solution.
(2)
It's possible to have different quadratic equations with the same solution, because
A*[x^2 -(a+b)x + ab]=0, A could vary as any number, so the quadratic equations are different