Answer:
[tex]x=-\frac{3\sqrt{2}}{2},\frac{3}{4},\frac{3\sqrt{2} }{2}[/tex]
Step-by-step explanation:
Given expression is,
f(x) = 8x³ - 6x² - 36x + 27
For zeros of the function,
f(x) = 0
8x³ - 6x² - 36x + 27 = 0
2x²(4x - 3) - 9(4x - 3) = 0
(2x² - 9)(4x - 3) = 0
(2x² - 9) = 0
x² = [tex]\frac{9}{2}[/tex]
x = [tex]\pm\frac{3}{\sqrt{2}}[/tex]
x = [tex]\pm \frac{3\sqrt{2}}{2}[/tex]
Or (4x - 3) = 0
x = [tex]\frac{3}{4}[/tex]
Therefore, all zeros of the given functions are [tex]x=-\frac{3\sqrt{2}}{2},\frac{3}{4},\frac{3\sqrt{2} }{2}[/tex].
