# Solving Quadratic Equation: Find Roots of m+ni & m-ni

• thereddevils
In summary, if one of the roots of a quadratic equation is m+ni, then the other root is m-ni. This can be shown by expanding the equation ax^2+bx+c=0 and setting it equal to zero, and then demonstrating that m-ni also satisfies the equation.
thereddevils

## Homework Statement

If one of the roots of the quadratic equation, ax^2+bx+c=0 is m+ni, show that the other root is m-ni.

## The Attempt at a Solution

How do i actually show this? I mean it's a well known fact and a direct outcome of the quadratic formula. Is this valid?

(x-(m+ni))(x-(m-ni))=0

then x-2m+m^2+n^2=0

thereddevils said:

## Homework Statement

If one of the roots of the quadratic equation, ax^2+bx+c=0 is m+ni, show that the other root is m-ni.

## The Attempt at a Solution

How do i actually show this? I mean it's a well known fact and a direct outcome of the quadratic formula. Is this valid?

(x-(m+ni))(x-(m-ni))=0

then x-2m+m^2+n^2=0
The last equation above is not correct. For one thing, there should be an x2 term.

You are given that m + ni is a root of the equation ax2 + bx + c = 0, so it should be true that a(m + ni)2 + b(m + ni) + c = 0.

Expand the stuff on the left and you will get a complex number that must be zero.

Now, what do you need to do to show that m - ni is also a solution of the same quadratic equation?

Mark44 said:
The last equation above is not correct. For one thing, there should be an x2 term.

You are given that m + ni is a root of the equation ax2 + bx + c = 0, so it should be true that a(m + ni)2 + b(m + ni) + c = 0.

Expand the stuff on the left and you will get a complex number that must be zero.

Now, what do you need to do to show that m - ni is also a solution of the same quadratic equation?

thanks Mark!

## 1. How do you solve a quadratic equation?

To solve a quadratic equation, you can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a. Plug in the values of a, b, and c from your equation and solve for x.

## 2. What are the roots of a quadratic equation?

The roots of a quadratic equation are the values of x that make the equation true. In the form of ax^2 + bx + c = 0, the roots are given by the solutions of the quadratic formula.

## 3. How do you find complex roots of a quadratic equation?

To find complex roots, you can use the quadratic formula and solve for x. If the discriminant (b^2 - 4ac) is negative, there will be complex roots in the form of a+bi and a-bi.

## 4. Can you use the quadratic formula to find roots of m+ni and m-ni?

Yes, the quadratic formula can be used to find the roots of any quadratic equation, including those in the form of m+ni and m-ni. Simply plug in the values of a, b, and c from the equation and solve for x.

## 5. What is the discriminant in a quadratic equation?

The discriminant is the part of the quadratic formula underneath the square root sign: b^2 - 4ac. It is used to determine the nature of the roots of the equation. If the discriminant is positive, there will be two real roots. If it is zero, there will be one real root. And if it is negative, there will be two complex roots.

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