If the roots of ax^{2}+bx+c=0 are \frac{3}{2},\frac{4}{3} then (a+b+c)^{2} =

Answered question

2021-10-11

 

If the roots of ax2+bx+c=0 are 32,43 then (a+b+c)2=

 

Answer & Explanation

Jeffrey Jordon

Jeffrey Jordon

Expert2021-10-21Added 2605 answers

Use the Vieta's theorem

x2+px+q=0

where

p=x1+x2

q=x1×x2

Let x1=32 and x2=43

So,

p=32+43=9+86=176

q=32×43=126=2

Our quadratic equation: x2176x+2=0

Then, let's find (a+b+c)2

where a=1, b=176, c=2

(1+(176)+2)2=(3176)2=(16)2=136

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