I'd like to know how to find relations between coefficients of a polynomial p(x) so that equation p(x) = 0 has only real roots.(adsbygoogle = window.adsbygoogle || []).push({});

For example I have quadratic equation:

x[tex]^{2}[/tex]+px+q = 0

then the Discriminant must be >= 0 so p[tex]^{2}[/tex] >= 4q

But I need to find it for equations of higher power of x (like 6), without having the formula for exact solutions - I know it's not possible to solve polynomial equations of order 6 and more.

It may be complicated if there are too many coefficients (there are 5 in 6th order pol.), but they just all depend just on one constant r, so it is like a5 = 2r, a4 = r[tex]^{2}[/tex], a3 = 1/r, and so on, and I need to know for which values of r the equation has only real roots.

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# Polynomial Equation

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