# What is a if ax^2 - 16x + 32 = 0 has only complex roots.

*print*Print*list*Cite

### 1 Answer

The roots of a quadratic equation ax^2 + bx + c = 0 are given by `(-b+-sqrt(b^2-4ac))/(2a)` . They are complex when b^2 - 4ac < 0

For the equation ax^2 - 16x + 32 = 0, the roots are complex when (-16)^2 - (4*a*32) < 0

=> 256 < 128a

=> 2 < a

**The roots of the given equation are complex for **`a in (-oo, 2)`