Solve the non-linear equation \$x^3 - 5x^2 + 6x = 0\$.

Rewrite the equation into quadratic form

\$x(x^2 - 5x + 6) = 0\$

x = 0 and \$x^2 - 5x + 6 = 0\$

The quadratic formulae

\$ x = (- b ± \sqrt(b^2 - 4ac)) / (2a) \$

Plug in the corresponding values using the quadratic formulae

Where a = 1, b = - 5, and c = 6

\$x = (-(- 5) ± sqrt ((-5)^2 - 4(1)(6))) / (2(1))\$

\$x = (5 ± sqrt (1)) / 2\$

The two possible answers are

\$x = (5 + 1) / 2 \$ and \$x = (5 - 1) / 2\$

x = 3 and x = 2

Therefore, the solutions to the equation is \$x^3 - 5x^2 + 6x = 0\$ are x = 0, x = 2, and x = 3.

Option A, x = - 2 and x = - 3, does not satisfy the equation when substituted back into \$x^3 - 5x^2 + 6x = 0\$, so it is not correct

x = 0, x = - 2, and x = - 3

It is not correct because it provides the values x = 2 and x = 3, but it misses the solution x = 0

x = 2 and x = 3

Option C, x = 1 and x = - 2, is incorrect because x = 1 is not a solution to the equation

x = 1 and x = - 2

This is correct as it includes all the accurate roots of the provided equation

x = 0, x = 2, and x = 3

Option

D

Can you summarize what you’ve understood in the above steps?