ANSWER
-1.0, 1.0
EXPLANATION
The given polynomial function is
[tex]f(x) = 2 {x}^{4} - {x}^{3} + x - 2[/tex]
According to the Rational Roots Theorem, the possible roots of this function are;
[tex] \pm1,\pm \frac{1}{2} [/tex]
We now use the Remainnder Theorem to obtain;
[tex]f(1) = 2 {(1)}^{4} - {(1)}^{3} + 1 - 2[/tex]
[tex]f(1) = 2 - 1+ 1 - 2 = 0[/tex]
[tex]f( - 1) = 2 {( - 1)}^{4} - {( - 1)}^{3} - 1 - 2[/tex]
[tex]f( - 1) = 2 + 1 - 1 - 2 = 0[/tex]
But;
[tex]f( \frac{1}{2} ) = - 1.5[/tex]
[tex]f( - \frac{1}{2} ) = - 2.25[/tex]
Since f(1)=0 and f(-1)=0, the real zeros to the nearest tenth are:
-1.0 and 1.0
