SOLUTION: Write a quadratic equation with the roots + or - radical5/4. write equation in the form ax^2+bx+c=0 where a, b, and c are integers. thanks.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Write a quadratic equation with the roots + or - radical5/4. write equation in the form ax^2+bx+c=0 where a, b, and c are integers. thanks.      Log On


   

Question 399248: Write a quadratic equation with the roots + or - radical5/4. write equation in the form ax^2+bx+c=0 where a, b, and c are integers.

thanks.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Use the fact that x-r is a factor of a polynomial if and only if r is a root. Since 5/4 and -5/4 are the roots, then the polynomial is

%28x-5%2F4%29%28x%2B5%2F4%29+=+x%5E2+-+25%2F16

This polynomial has the same zeros as 16x%5E2+-+25 (the coefficients are integers in this case) so this is the desired polynomial. We could multiply this by some other integer to obtain a similar polynomial, for example, 48x%5E2+-+75.