Question

P(x)=3x2-x-4
Then alpha + bita by alpha*bita =

Answer 1

-
`(1)/(4)`

Explanation:

Given

P(x) = 3x² - x - 4

with a = 3, b = - 1 and c = - 4

If α and β are the roots of the quadratic then

α + β = -
`(b)/(a)` and αβ =
`(c)/(a)` , thus

α + β = -
`(-1)/(3)` =
`(1)/(3)` and αβ = -
`(4)/(3)`

Thus

α + β by αβ

=
`((1)/(3) )/(-(4)/(3) )` =
`(1)/(3)` × -
`(3)/(4)` = -
`(1)/(4)`

Answer 2

`= ( ( - b)/(a) )( (c)/(a) )`

`= ( ( 1)/(3) )( ( - 5)/(3) )`

`= ( - 5)/(9)`