If-is-a-real-root-of-2x-3-3x-2-6x-6-0-then-find-where-denotes-the-greatest-integer-function-

Question Number 20368 by Tinkutara last updated on 26/Aug/17

If α is a real root of 2 x^{3} - 3 x^{2} + 6 x + 6 = 0,

then find [α] where [\cdot] denotes the

greatest integer function .

Commented by ajfour last updated on 26/Aug/17

f (x) = 2 x^{3} - 3 x^{2} + 6 x + 6

f^{'} (x) = 6 x^{2} - 6 x + 6

= 6 {(x - \frac{1}{2})}^{2} + \frac{9}{2} > 0

H e n c e o n l y o n e r e a l r o o t .

f^{'} (x) > 0 a n d f (0) = 6

s o r o o t α < 0

f (- 1) = - 5, s o α > - 1

\Rightarrow - 1 < α < 0

\Rightarrow [α] = - 1 .

Commented by Tinkutara last updated on 26/Aug/17

Thank you very much Sir!