How many real solutions does the equation x5 + 2x3 + 8x2 + 16 = 0 have?
Choose the correct choice from the following:
A) 0 B) 1 C) 2 D) 3 E) 5

Rationale: note that x 5 + 2 x 3 + 8 x 2 + 16 = ( x 3 + 8 ) ( x 2 + 2 ) = ( x + 2 ) ( x 2 - 2 x + 4 ) ( x 2 + 2 ) . since the quadratic equations x 2 - 2 x + 4 = 0 and x 2 + 2 = 0 have no real solutions , the original equation has just one real solution , x = - 2 . correct answer b
Answer: B