Question

Math Finding the root (30points!!!!!)

Answer 1

p =
`(12)/(7)`

Explanation:

let the root be α then the other root is 3α

The sum of the roots of a quadratic equation is

α + 3α = -
`(b)/(a)` = -
`(-8)/(7)` =
`(8)/(7)`

Thus 4α =
`(8)/(7)` ( divide both sides by 4 )

α =
`(2)/(7)`

The product of the roots of a quadratic equation are

α × 3α =
`(c)/(a)` =
`(p)/(7)`, that is

3α² =
`(p)/(7)` ← substitute value of α

3 × (
`(2)/(7)` )² =
`(p)/(7)`

3 ×
`(4)/(49)` =
`(p)/(7)`

`(12)/(49)` =
`(p)/(7)` ( cross- multiply )

49p = 84 ( divide both sides by 49 )

p =
`(84)/(49)` =
`(12)/(7)`