Question

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

Answer 1

Answer:

The value of $m$ is -30.

Step-by-step 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:

$x^{2}+\frac{m}{27}\cdot x + \frac{8}{27} = 0$ (1)

$-x^{2}-x = \frac{m}{27}$ (2)

$x^{3} = \frac{8}{27}$ (3)

From (3) we find the least root:

$x = \sqrt [3]{\frac{8}{27}}$

$x = \frac{2}{3}$

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

$m = -27\cdot (x^{2}+x)$

$m = -30$