4x³ - 20x² + 24x = 0
4x(x² - 5x + 6) = 0
4x(x - 2)(x - 3) = 0
4x = 0 x - 2 = 0 x - 3 = 0
x = 0 x = 2 x = 3
Answer: 0, 2, 3
Factoring and solving a quadratic equation, it is found that the roots of the equation are:
[tex]x = 0[/tex]
[tex]x = 2[/tex]
[tex]x = 3[/tex]
The equation given is:
[tex]4x^3 - 20x + 24x = 0[/tex]
Factoring the common term:
[tex]4x(x^2 - 5x + 6) = 0[/tex]
For the roots:
[tex]4x = 0 \rightarrow x = 0[/tex]
Or
[tex]x^2 - 5x + 6 = 0[/tex]
Which is a quadratic equation with coefficients [tex]a = 1, b = -5, c = 6[/tex], and then:
[tex]\Delta = (-5)^{2} - 4(1)(6) = 1[/tex]
[tex]x_{1} = \frac{-(-5) + \sqrt{1}}{2} = 3[/tex]
[tex]x_{2} = \frac{-(-5) - \sqrt{1}}{2} = 2[/tex]
Thus, the other two roots are [tex]x = 2[/tex] and [tex]x = 3[/tex].
A similar problem is given at https://brainly.com/question/11513376
