Question

Approximate the real zeros of f(x) = 2x^4 - x^3 + x-2 to the nearest tenth

Answer 1

Answer:

-1.0, 1.0

Step-by-step 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 \frac{1}{2}

We now use the Remainder 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( \frac{1}{2} ) = - 1.5

f( - \frac{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