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

a - 1,1

c. 0,1

b. - 2. - 1

d - 1,0

-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