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Write a quadratic equation for which the sum of the roots is equal to the product of the roots.

$x^{2}-k x+k=0$

Algebra

Chapter 5

QUADRATIC FUNCTIONS AND COMPLEX NUMBERS

Section 7

Sum and Product of the Roots of a Quadratic Equation

Equations and Inequalities

Quadratic Functions

Complex Numbers

Polynomials

Missouri State University

Campbell University

Oregon State University

Idaho State University

Lectures

01:32

In mathematics, the absolu…

01:11

01:06

Write a quadratic equation…

01:00

01:07

01:02

03:42

01:33

01:31

Show that the sum of the r…

00:26

What are the roots of a qu…

01:01

01:04

03:19

Use the quadratic formula …

02:21

One root of a quadratic eq…

03:10

01:16

06:06

02:35

02:06

01:54

Find the sum and the produ…

all right. We need an equation where the some and the product is the same. And so immediately, I just kind of look at this something for something and something time something has to be the same thing and is like, well, four would work because two plus two is four and two times two is four. And so that was the one that I chose. And there's several different options. I think this is the easiest one. So if we know Route one is equal to two in route to is equal to two, which is possible. If you have a quadratic equation that looks something like this, we're just touches right there. Then we can make this equation. So if four is equal to negative, be over a let's say, is one, then that would mean be would be a negative four, because negative for over one if we put another negative there would get us that for that. We want the positive for, And so then if see, over a is equal to four and is equal one. That means that C is equal to four and so we can have an A B and C if I see value, we can make an equation X squared minus four X plus four equal to zero and we get this whole thing is gonna work out.

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