Given the functions [tex]H(x) = x^2 + 1[/tex] and [tex]K(x) = -(x^2) + 4[/tex]. If [tex]K(H(x)) = 0[/tex], what are the roots/solutions?

A. ±i√3
B. ±i
C. ±2
D. ±1
E. ±1, ±i√3

H ( x ) = ( x 2 ) + 1 an d K ( x ) = − ( x 2 ) + 4. K ( H ) = − ( H 2 ) + 4 = − ( x 2 + 1 ) 2 + 4 = 4 − ( x 2 + 1 ) 2 = . = 2 2 − ( x 2 + 1 ) 2 = ( 2 − x 2 − 1 ) ( 2 + x 2 + 1 ) = ( 1 − x 2 ) ( 3 + x 2 ) = . = ( 1 − x ) ( 1 + x ) ( x 2 − 3 ⋅ i 2 ) = ( 1 − x ) ( 1 + x ) ( x − 3 ​ ⋅ i ) ( x + 3 ​ ⋅ i ) K ( H ) = 0 ⇔ ( 1 − x ) ( 1 + x ) ( x − 3 ​ ⋅ i ) ( x + 3 ​ ⋅ i ) = 0 x = 1 or x = − 1 or x = 3 ​ ⋅ i or x = − 3 ​ ⋅ i A n s . e .

Answered by kate200468 | 2024-06-10

The roots of the equation K ( H ( x )) = 0 are ± 1 and ± i 3 ​ . The correct answer is option E: ± 1 , ± i 3 ​ .
;

Answered by kate200468 | 2024-12-23