State how many complex and real zeros the function has.
-$$f ( x ) = x ^ { 3 } - 15 x ^ { 2 } + 75 x - 125$$
A) 3 complex zeros; 1 real
B) 3 complex zeros; none real
C) 3 complex zeros; all 3 real
D) 3 complex zeros; 2 real

Question

Quizplus · Accepted Answer

The function is a cubic polynomial, which means it has exactly 3 complex zeros. Since all coefficients are real, any complex zeros must come in conjugate pairs. However, a cubic function cannot have just one complex zero (it would need two, which is impossible here), so all 3 zeros must be real.

State How Many Complex and Real Zeros the Function Has f(x)=x3−15x2+75x−125f ( x ) = x ^ { 3 } - 15 x ^ { 2 } + 75 x - 125f(x)=x3−15x2+75x−125

State How Many Complex and Real Zeros the Function Has $f ( x ) = x ^ { 3 } - 15 x ^ { 2 } + 75 x - 125$