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# help

+1
112
3

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

Dec 31, 2018

#2
+4221
+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!

Dec 31, 2018
edited by tertre  Dec 31, 2018

#1
+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
+4221
+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!

tertre Dec 31, 2018
edited by tertre  Dec 31, 2018
#3
+100549
+1

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

CPhill  Dec 31, 2018