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Given the quadratic equation $a x^{2}+b x+c=0$ and $c x^{2}+b x+a=0$ prove that the roots of one equation are the reciprocals of the roots of the other equation.

Algebra

Chapter 0

Reviewing the Basics

Section 4

The Quadratic Formula and Applications

Equations and Inequalities

Campbell University

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

01:27

Let $a, c \neq 0 .$ Show t…

06:21

Find a quadratic equation …

00:59

Show that the two roots of…

03:39

Show that the real solutio…

03:41

If the ratio of the roots …

03:19

Use the quadratic formula …

03:16

Find the quadratic equatio…

03:12

If the sum of the roots of…

04:50

If there is a common root …

We have these two quadratic aquariums and according to the quadratic formula, their solutions this and this And for the second aquarium will resume its solution. X one bar in X two bar. And next we know this formula and X one times x. toolbar equals these times disease. And according to this formula, the denominator can be simplified as these. And this is just a voice. They were for a C vertical squad and the result of X. Two times X one bar is similar And the result is also one. So this is to see X one is a reciprocal of X. two bar And X two is the reciprocal of X. one member. And this is just what we want to prove.

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