Question 399248
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


{{{(x-5/4)(x+5/4) = x^2 - 25/16}}}


This polynomial has the same zeros as {{{16x^2 - 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^2 - 75}}}.