The four roots are:1 + 2i, 1 - 2i, 3i and -3i.
If you have two equations give AND one parametric equation why do you need to find yet another equation?
to find a linear equation the roots must have been given in the question. to check whether its correct or not use this method. x2-(SOR)x+POR=0. SOR = sum of roots, POR = product of roots. if your SOR and POR is similar to your final answer, then the solution is correct
z5 is an expression, not an equation and so cannot have roots.
Do mean find the polynomial given its roots ? If so the answer is (x -r1)(x-r2)...(x-rn) where r1,r2,.. rn is the given list roots.
To find the roots (solutions) of a quadratic equation.
Write an algorithm to find the root of quadratic equation
to find a linear equation the roots must have been given in the question. to check whether its correct or not use this method. x2-(SOR)x+POR=0. SOR = sum of roots, POR = product of roots. if your SOR and POR is similar to your final answer, then the solution is correct
If you have two equations give AND one parametric equation why do you need to find yet another 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.
Do mean find the polynomial given its roots ? If so the answer is (x -r1)(x-r2)...(x-rn) where r1,r2,.. rn is the given list roots.
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.
You can find the roots with the quadratic equation (a = 1, b = 3, c = -5).