Question

Find the sum and product of the roots. 7x 2 - 3x - 9 = 0

Answer 1

7x^2-3x-9=0
applying the quadratic formula we get:
x=[-b+/-sqrt(b^2-4ac)]/(2a)
x=[-(-3)+/-sqrt((-3)^2-4*7*(-9))]/(2*7)
x=[3+/-sqrt(9+252)]/14
x=[3+/-sqrt162]/14
hence
x=[3+/-16.1555]/14
x=1.3682 or -0.9396
thus the sum of the roots will be:
(1.3682+(-0.9396))=0.4286
the product will be:
(1.3682)(-0.9396)
=-1.28556

Answer 2

Sum of the roots is
`(3)/(7)`

Product of the roots is
`-(9)/(7)`

Explanation:

In a quadratic equation ax² + bx + c = 0,

Sum of the roots =
`-(b)/(a)`

And, product of the roots =
`(c)/(a)`

Here, the given quadratic equation,

`7x^2-3x-9=0`

Hence,

Sum of the roots =
`-(-3)/(7)` =
`(3)/(7)`

Product of the roots =
`(-9)/(7)` =
`-(9)/(7)`