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How many real roots will a 3rd degree polynomial have?
A third degree polynomial could have one or three real roots.
Why is roots of even or odd hurwitz polynomial found on the jw axis only?
Actually, the roots of a Hurwitz polynomial are in the left half of the complex plain, not on the imaginary axis. As for the reason, that is because the polynomial is DEFINED to be one that has that kind of roots.
How do you factor a polynomial with the equation of 6A2 - B 2?
The given polynomial does not have factors with rational coefficients.
How do you determine the number of real roots in a polynomial?
For a general polynominal, the cubic, quartic, and greater formulæ are too hellishly hard to work with, so you would need to plot the function or use Newton's/somesuch method to count the real roots by hand. If the polynomial has integral roots, you can use synthetic division to peel off the degrees to see if they factor wholely into binominals; then all roots will be real and explicit. Good luck:
What are some similarities and differences between quartic and cubic functions?
The similarities are that they are polynomial functions and therefore continuous and differentiable.A real cubic will has an odd number of roots (and so must have a solution), a quartic has an even number of roots and so may have no solutions.
