Given:
\[ H(x) = (x^2) + 1 \]
\[ K(x) = -(x^2) + 4 \]

If \( K(H) = 0 \), what are the roots/solutions?

A. \(\pm i\sqrt{3}\)
B. \(\pm i\)
C. \(\pm 2\)
D. \(\pm 1\)
E. \(\pm 1, \pm i\)

H ( x ) = x 2 + 1 ; K ( x ) = − x 2 + 4 K ( H ) = K ( x 2 + 1 ) = − ( x 2 + 1 ) 2 + 4 = 0 ( x 2 + 1 ) 2 = 4 ⟺ x 2 + 1 = ± 4 ​ x 2 + 1 = − 2 or x 2 + 1 = 2 ∣ s u b t r a c t 1 f ro m b o t h s i d es x 2 = − 3 or x 2 = 1 x = ± i 3 ​ or x = ± 1 ​

Answered by Anonymous | 2024-06-10

The roots of the equation K ( H ) = 0 are ± i 3 ​ and ± 1 . Therefore, the possible answers are A and D. However, since A is presented as a single option, we highlight the roots ± i 3 ​ .
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Answered by Anonymous | 2025-05-17