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What is the sum of the squares of the roots of \(18x^2 +21x - 400?\)?

 Feb 20, 2019
 #1
avatar+19832 
+1

Quadratic formula....

roots   -5.333  and  4.166     squared and added together = 45.79

 Feb 20, 2019
 #2
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Sorry but that was wrong

 Feb 20, 2019
 #3
avatar+19832 
+1

I assumed this was    18x^2 +21x -400 = 0      Yah?

ElectricPavlov  Feb 20, 2019
 #4
avatar+104937 
+3

The sum of the roots = -b / a =  -21/18  =  -7/6

 

The product of the roots = c / a = -400/18 = -200/9

 

Let the roots be  p, q

 

p + q =   -7/6    

 

pq = -200/9    ⇒   2pq = -400/9

 

(p + q)^2 =   49/36

 

p^2 + 2pq + q^2 = 49/36

 

p^2 +  (-400/9) + q^2  = 49/36

 

p^2 + q^2 =  49/36 + 400/9

 

p^2 + q^2 =  [ 49 + 1600] / 36  = 1649 / 36   ≈   45.8....just as EP found !!!!

 

 

cool cool cool

 Feb 20, 2019
edited by CPhill  Feb 20, 2019

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