+0  
 
-2
31
1
avatar+817 

The roots of the equation $2x^2 - 5x - 4 = -x^2 - 7x + 6$ can be written in the form $x = \frac{m \pm \sqrt{n}}{p}$, where $m$, $n$, and $p$ are positive integers with a greatest common divisor of $1$. What is the value of $n$?

 Aug 21, 2023
 #1
avatar+129659 
+1

\(x = \frac{m \pm \sqrt{n}}{p}\)

 

 

2x^2 - 5x - 4 = -x^2 -7x + 6       rearrange as

 

3x^2 + 2x - 10  =  0 

 

The  discriminant =  

 

(2)^2  - 4(3)(-10)  =  

 

4 + 120  =  

 

124

 

sqrt (124)  =sqrt (31 * 4)  =  2 sqrt (31)

 

So

 

x =  [ -2  ± 2 sqrt (31)  ]  / ( 2 * 3)  =    [ -1  ± sqrt (31)] / 3

 

n = 31

 

cool cool cool

 Aug 22, 2023

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