The nature of the roots may be determined by solving for the value of the discriminant.
discriminant = positive : 2 distinct real roots
= 0 : 2 equal real roots
= negative : 2 distinct unreal roots
given ax² +bx +c = 0
discriminant = b² -4ac
For x²+6x+3=0,
discriminant = 6² - 4(1)(3)
= 36 -12
= 28
The discriminant of x²+6x+3=0 is positive, therefore it has 2 distinct real roots.
