Answer:
The Solutions are distinct and rational
Step-by-step explanation:
Given the general form of a quadratic equation: ax²+bx+c=0
The discriminant D=b²-4ac is used to determine the nature of the roots of the quadratic equation.
There are three cases:
1. If b² - 4ac > 0
The quadratic equation has two real, distinct (different) roots.
2.If b² - 4ac < 0
The quadratic equation has no real roots. i.e. It has complex roots
3. If b² - 4ac = 0
The quadratic equation has two real, identical roots.
Given our equation:
5x²+11x+6=0
a=5, b=11, c=6
The discriminant:
D=b²-4ac=11²-4(5)(6)=1
Since D=1>0, the roots of the equation are real and distinct.
