Mentor... i solved many quadratic, cubic and quartic equations and whenever i got a complex solution, one of the other solutions was always a complex conjugate... This made me think that the result was true for all polynomial and hence the question... Thanks to all of you, i have finally been...
Prove that all polynomials with real coefficients, having complex roots can occur in complex conjugates only.
It's easy to prove in a quadratic equation...
## ax^{2} + bx + c = 0 ##
## \displaystyle x = \frac{-b \pm \sqrt(b^2 - 4ac)}{2a} ##
But how to prove the same in general?
Please...
Sir, could the solution be a little more general?... i.e. to help me prove this property is universally applicable for all the polynomials with real coefficients.
How to explain that the case where all roots are equal to one is a minimum?
Prove that product of sum of roots and sum of reciprocal of roots of a polynomial with degree n is always greater than or equal to n2.
I tried the same on a polynomial of degree 4:
ax4+bx3+cx2+dx+e = 0
Let the roots be p, q, r, and s
The following equations show the relation of roots to...