determinant: [tex]\sqrt{b^2-4ac}[/tex]
(a) [tex]x^2+4x+5=0\\D=4^2-4\cdot1\cdot5={-4}\\D<0[/tex]
D<0 means there are no real roots. there are two complex roots with imaginary components.
(b) D=16+20=36>0
D>0 means there are two real roots
(c) D = 20^2-4*4*25 = 0
D=0 means there is one real root with multiplicity 2
