Question

How many and of which kind of roots does the equation f(x) = 2x4 – 9.23 + 1722 – 16x + 6 have?

A. 4 real
OB. 4 real; 4 complex
C. 2 real; 2 complex
OD. 4 complex
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Answer 1

D, it admits 4 complex roots

Explanation:

Based on what you've written;

f(x) can be rewritten by adding the light terms together as;

f(x)=2x⁴-16x+1768.68

By graphing this function on an app, since i cannot possibly simplify this equation or use a calculator;

we observe that this function does not intersect the x-axis at any point, hence it does not admit any real roots.

So your answer must be D.

ps: Regardless if you forgot any x's in your equation and if f(x) was actually defined by,

f(x)=2x⁴-9.32x³+1772x²-16x+6

This equation also admits 4 complex roots and does not intersect the x-axis