Create a quadratic from two values?

[Guru]

When solving an equation in the form



using:



we get two answers. Agreed?

Now, what I want is a way of creating an equation in the form


from two values of x

eg x=14.468 , x=52.583

Any suggestions?

[VBAhack]

You have 2 equations in 3 unknowns, so there are potentially infinitely many solutions. If you are willing to choose c arbitrarily, then you can find a solution by straightforward substitution because the problem reduces to 2 equations in 2 unknowns.

a = c/(x₁*x₂)

b = -c/x₂ - a*x₂ = -c(1/x₂ + 1/x₁)

[Logophobic]

eg x=14.468, x=52.583
(x - 14.468)(x - 52.583) = 0
x² - 67.051*x + 760.770844 = 0

If you want 'a' to be anything other than 1, simply multiply through by whatever value you want 'a' to be.

[Guru]

That's perfect!

Thanks