Question

Approximate the real zeros of f(x)=2x^4-x^3+x-2 to the nearest tenth. a. , 1 c. 0, 1 b. , d. , 0 Please select the best answer from the choices provided

Answer 1

D

Explanation:

Just took the test

Answer 2

ANSWER

-1.0, 1.0

EXPLANATION

The given polynomial function is


`f(x) = 2 {x}^(4) - {x}^(3) + x - 2`

According to the Rational Roots Theorem, the possible roots of this function are;


`\pm1,\pm (1)/(2)`

We now use the Remainnder Theorem to obtain;


`f(1) = 2 {(1)}^(4) - {(1)}^(3) + 1 - 2`


`f(1) = 2 - 1+ 1 - 2 = 0`


`f( - 1) = 2 {( - 1)}^(4) - {( - 1)}^(3) - 1 - 2`


`f( - 1) = 2 + 1 - 1 - 2 = 0`

But;


`f( (1)/(2) ) = - 1.5`


`f( - (1)/(2) ) = - 2.25`

Since f(1)=0 and f(-1)=0, the real zeros to the nearest tenth are:

-1.0 and 1.0