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The roots of an equation means the solutions of an equation. Different methods have been developed for different kinds of equation. It is not possible to give an overview in one or two paragraphs, but in simpler cases, the same operation is done on both sides of the equation, with the aim of "isolating" the variable you are solving for, that is, having it alone on one side. In some complicated cases, no "explicit" solutions exist, and "numerical" solutions have to be used; this basically means using trial-and-error.

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Q: How do you find the roots of and equation?

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z5 is an expression, not an equation and so cannot have roots.

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In numerical analysis finding the roots of an equation requires taking an equation set to 0 and using iteration techniques to get a value for x that solves the equation. The best method to find roots of polynomials is the Newton-Raphson method, please look at the related question for how it works.

To find the roots (solutions) of a quadratic equation.

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If the quadratic is ax2 + bx + c = 0 then the product of the roots is c/a.

This quadratic equation has no real roots because its discriminant is less than zero.

A quadratic equation has two roots. They may be similar or dissimilar. As the highest power of a quadratic equation is 2 , there are 2 roots. Similarly, in the cubic equation, the highest power is 3, so it has three equal or unequal roots. So the highest power of an equation is the answer to the no of roots of that particular equation.

When you need to find the roots of a quadratic equation and factorisation does not work (or you cannot find the factors). The quadratic equation ALWAYS works. And when appropriate, it will give the imaginary roots which, judging by this question, you may not yet be ready for.

2 roots

It will then have 2 different roots If the discriminant is zero than it will have have 2 equal roots

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