Answer:
Step-by-step explanation:
f(x) = 2x³ + ax² - 7a²x - 6a³
= 2x³ - 2a²x + ax² - a³ - 5a²x - 5a³
= 2x(x² - a²) + a(x² - a²) - 5a²(x+a)
= (2x+a)(x - a)(x + a) - 5a²(x + a)
= (x + a)[(2x + a)(x - a) - 5a²]
= (x + a)(2x² - ax - 6a²)
= (x + a)(2x + 3a)(x - 2a)
x-a is the factor of the equation and x + a is not a factor of the equation,
All the roots of the equation are x + a, 2x+3a, x-2a.
"In algebra, a cubic equation in one variable is an equation of the form
ax^3+bx^2+cx+d=0
in which a is nonzero.
The solutions of this equation are called roots of the cubic function defined by the left-hand side of the equation. If all of the coefficients a, b, c, and d of the cubic equation are real numbers, then it has at least one real root (this is true for all odd-degree polynomial functions). "
Given equation is [tex]f(x) = 2x^3 + ax^2 - 7a^2x - 6a^3[/tex]
Now,
[tex]f(x) = 2x^3 + ax^2 - 7a^2x - 6a^3\\\\= 2x^3 - 2a^2x + ax^2 - a^3 - 5a^2x - 5a^3\\\\= 2x(x^2 - a^2) + a(x^2 - a^2) - 5a^2(x+a)\\\\= (2x+a)(x - a)(x + a) - 5a^2(x + a)\\\\= (x + a)[(2x + a)(x - a) - 5a^2]\\\\= (x + a)(2x^2 - ax - 6a^2)\\\\= (x + a)(2x + 3a)(x - 2a)[/tex]
Hence, the roots of the equation are x + a, 2x +3a, x - 2a.
To know more about cubic equation here
https://brainly.com/question/13730904
#SPJ2
