Solve `x^2+3x+5=0`

Options

A. only purely imaginary roots
B. all real roots
C. two real and two purely imaginary roots
D. neither real nor purely imaginary roots

Answer

A, D

Explanation

Sicne `b=0` for `p(x)=ax^(2)+bx+c` as roots are pure imaginary.
`impliesx=+-sqrt((-c+-isqrt(c)))/a)`, which are clearly neigher pure real nor pure imaginary as `c!=0`