Question

Find the sum and product of the roots. 3x 2 - 4x - 7 = 0

Answer 1

sum of the roots = -b/a = -(-4)/ 3 = 4/3

product = c/a = -7/3

Answer 2

Part 1) The sum of the roots is
`4/3`

Part 2) The product of the roots is
`-7/3`

Explanation:

Step 1

Find the roots

we have

`3x^(2)-4x-7=0`

The formula to solve a quadratic equation of the form
`ax^(2) +bx+c=0` is equal to

`x=\frac{-b(+/-)\sqrt{b^(2)-4ac}} {2a}`

in this problem we have

`3x^(2)-4x-7=0`

so

`a=3\\b=-4\\c=-7`

substitute in the formula

`x=\frac{-(-4)(+/-)\sqrt{-4^(2)-4(3)(-7)}} {2(3)}`

`x=\frac{4(+/-)\sqrt{16^(2)+84}} {6}`

`x=\frac{4(+/-)10} {6}`

`x1=\frac{4+10} {6}=7/3`

`x2=\frac{4-10} {6}=-1`

Step 2

Find the sum of the roots

`x1+x2=(7/3)-1=4/3`

Step 3

Find the product of the roots

`x1*x2=(7/3)*(-1)=-7/3`