Answer:
The value of [tex]m[/tex] is -30.
Step-by-step explanation:
Let [tex]27\cdot x^{2}+m\cdot x +8 = 0[/tex], we notice that expression is a second order polynomials. We can rearrange the polynomial and use factorization to calculate all roots:
[tex]x^{2}+\frac{m}{27}\cdot x + \frac{8}{27} = 0[/tex] (1)
[tex]-x^{2}-x = \frac{m}{27}[/tex] (2)
[tex]x^{3} = \frac{8}{27}[/tex] (3)
From (3) we find the least root:
[tex]x = \sqrt [3]{\frac{8}{27}}[/tex]
[tex]x = \frac{2}{3}[/tex]
By (2) we have the value of [tex]m[/tex]:
[tex]m = -27\cdot (x^{2}+x)[/tex]
[tex]m = -30[/tex]
