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Show that the real solutions of the equation $a x^{2}+b x+c=0$ are the negatives of the real solutions of the equation $a x^{2}-b x+c=0 .$ Assume that $b^{2}-4 a c \geq 0$

$$a x^{2}+b x+c=0, x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a} ; a x^{2}-b x+c=0, x=\frac{b \pm \sqrt{(-b)^{2}-4 a c}}{2 a}=\frac{b \pm \sqrt{b^{2}-4 a c}}{2 a}=-\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$$

Algebra

Chapter 1

Equations and Inequalities

Section 2

Quadratic Equations

Linear Functions

Quadratic Functions

Campbell University

Baylor University

University of Michigan - Ann Arbor

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they're given to war. Radic equations. The 1st 1 is X squared, plus B X plus C is equal to zero on, and the 2nd 1 is a X squared minus. B X plus E is equal to zero. Now, using the quadratic formula, let's find the value off rules. So both the given quadratic equations so for the 1st 1 will get X as equal toe minus B plus minus under load off B squared minus four multiplied with a multiplied but see divided by two multiplied with a, which gives us it's as equal toe minus being plus minus. Root off B squared minus four a. C. Divided by do it Such that B squared minus four A. C is always greater than equal to zero. Now. Similarly serving for the 2nd 1 we'll get X as equal to minus off minus B plus minus. Root off. Be square minus four multiplied with a multiplied with C divided by do it, which gives us ecstasy equal to B plus minus under root off B squared minus four a. C. Divided by two A. Such that over here also B squared minus four. A. C is greater than or equal to zero. Now, if we look at the roots of the first equation on, if you re light this, we can write X as equal to minus common B minus, plus under root off B squared minus four a. C divided by Do it now, since the square minus four aces already positive that we have already established is being given in the question. So that means from here we can say that X is equal toe negative off the routes off the second equation. So this is what we had to prove that the roads off the first equation is equal toe negative off the roots off second decoration hence approved.

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