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September 28th, 2019, 06:32 AM  #1 
Senior Member Joined: Dec 2015 From: somewhere Posts: 734 Thanks: 98  Quadratic polynomial
Find the quadratic equation which satisfies the condition $\displaystyle x_1 x_2 =x_1 +x_2$.

September 28th, 2019, 07:34 AM  #2 
Senior Member Joined: Jun 2019 From: USA Posts: 310 Thanks: 162 
I don't understand the problem statement. Quadratic equation in what? You could write the condition itself as $\displaystyle x_1 = \frac{x_2}{x_21}$ or $\displaystyle x_2 = \frac{x_1}{x_11}$ or $\displaystyle (x_11)(x_21)1 = 0$ Are any of those what you were looking for? 
September 28th, 2019, 08:00 AM  #3 
Senior Member Joined: Dec 2015 From: somewhere Posts: 734 Thanks: 98 
The equation is : $\displaystyle x^2 2x+2=0$. It satisfies the condition $\displaystyle x_1 x_2 = x_1 + x_2$. 
September 28th, 2019, 08:28 AM  #4  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,304 Thanks: 961 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
By Vieta's formula we have that $\displaystyle x_1 x_2 = \dfrac{c}{a}$ and $\displaystyle x_1 + x_2 =  \dfrac{b}{a}$ Thus $\displaystyle \dfrac{c}{a} = \dfrac{b}{a}$. Clearly then, c = b, so your quadratic will be $\displaystyle y = a x^2 + bx  b$. Your example is of the same form. Dan  
September 28th, 2019, 04:05 PM  #5 
Senior Member Joined: Sep 2016 From: USA Posts: 670 Thanks: 440 Math Focus: Dynamical systems, analytic function theory, numerics  The equation $x_1x_2 = x_1 + x_2$ Is equivalent to $x_1x_2  x_1  x_2 = 0$ and the left side of this is already a quadratic polynomial so I have no clue what you are asking.


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polynomial, quadratic 
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