Question

If one root is the square of the other in the equation 8+mx+27x²=0,find the value of m​

Answer 1

The value of
`m` is -30.

Explanation:

Let
`27\cdot x^(2)+m\cdot x +8 = 0`, we notice that expression is a second order polynomials. We can rearrange the polynomial and use factorization to calculate all roots:

`x^(2)+(m)/(27)\cdot x + (8)/(27) = 0` (1)

`-x^(2)-x = (m)/(27)` (2)

`x^(3) = (8)/(27)` (3)

From (3) we find the least root:

`x = \sqrt [3]{(8)/(27)}`

`x = (2)/(3)`

By (2) we have the value of
`m`:

`m = -27\cdot (x^(2)+x)`

`m = -30`