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What are the sum and product of the roots in 3x^2-4x-7

 Dec 31, 2018

Best Answer 

 #2
avatar+3987 
+2

A quicker way is to use Vieta's, where the sum of the roots are \(\frac{-b}{a}\) and the product of the roots are \(\frac{c}{a}.\)

 

In the expression \(3x^2-4x-7, \)   we attain \(a=3, b=-4\) , and \(c=-7.\)

 

Now, by plugging in our values, the sum of the roots is \(\frac{-(-4)}{3}=\frac{4}{3}.\)

 

Consequently, the product of the roots is \(\frac{-7}{3}.\)

 

Hope this helped!

 

smileysmiley

 Dec 31, 2018
edited by tertre  Dec 31, 2018
 #1
avatar
+2

Use quadratic formula to find the roots of x:

x =2 1/3

x = - 1

Their sum = 2 1/3 - 1 =1 1/3

Their product = 2 1/3 x - 1 =- 2 1/3

 Dec 31, 2018
 #2
avatar+3987 
+2
Best Answer

A quicker way is to use Vieta's, where the sum of the roots are \(\frac{-b}{a}\) and the product of the roots are \(\frac{c}{a}.\)

 

In the expression \(3x^2-4x-7, \)   we attain \(a=3, b=-4\) , and \(c=-7.\)

 

Now, by plugging in our values, the sum of the roots is \(\frac{-(-4)}{3}=\frac{4}{3}.\)

 

Consequently, the product of the roots is \(\frac{-7}{3}.\)

 

Hope this helped!

 

smileysmiley

tertre Dec 31, 2018
edited by tertre  Dec 31, 2018
 #3
avatar+98005 
+1

Thanks, tertre......this is a helpful theorem in many situations......

 

 

cool cool cool

CPhill  Dec 31, 2018

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