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.
z5 is an expression, not an equation and so cannot have roots.
To find the roots (solutions) of a quadratic equation.
The roots of the equation
If the discriminant of the quadratic equation is zero then it will have 2 equal roots. If the discriminant of the quadratic equation is greater than zero then it will have 2 different roots. If the discriminant of the quadratic equation is less than zero then it will have no roots.
Either "roots" or "solutions".
Write an algorithm to find the root of quadratic equation
for an 2nd order the roots are : [-b+-sqrt(b^2-4ac)]/2a
z5 is an expression, not an equation and so cannot have roots.
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.
This quadratic equation has no real roots because its discriminant is less than zero.
To find the roots (solutions) of a quadratic equation.
If the quadratic is ax2 + bx + c = 0 then the product of the roots is c/a.
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.
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.
You can find the roots with the quadratic equation (a = 1, b = 3, c = -5).
It will then have 2 different roots If the discriminant is zero than it will have have 2 equal roots
That depends on the equation.