does 4x^2+2x-1=0 have a real root, imaginary root or both?

Answer 1

x= [ - 2 ± √(4 + 16) ] / 8
x = [- 2 ± √(20) ] / 8
x = [- 2 ± 2√(5) ] / 8
x = (1/4) [- 1 ± √5 ]
Real roots.

Answer 2

Use the quadratic formular. for any expression in the form of:

y = ax^2 + bx + c

the roots can be found by:

x = [-b +/- sqrt (b^2 - 4ac)] / (2a)

The expression [b^2-4ac] determines whether you have real or imaginary roots (it is alwys one or the other, never both). The squart root of a positive number will give you real numbers (hence real roots) and that of a negative number will give you imaginary numbers (hence imagniary roots).