Question

How many no real complex roots does the polynomial f (x) = x^4 - x^2- 12 have?

A. 0
B. 1
C. 2
D. 3
E. 4

Answer 1

• 2 real roots
• 2 complex roots

Explanation:

f(x) factors as ...

... f(x) = (x² -4)(x² +3) = (x -2)(x +2)(x² +3)

The real roots are x = ±2.

The complex roots are x = ±i√3.

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We don't know what "no real complex roots" means. We suspect your answer may be C. 2.