### Mathematics Class X

Real Numbers
Polynomials
Arithmetic Progressions
Triangles
Coordinate Geometry
Introduction to Trigonometry
Circles
Constructions
Areas Related to Circles
Surface Areas and Volumes
Statistics
Probability

# Nature of Roots

From the quadratic formula, we can see that the two roots of the Quadratic Equation are –

[mathtype]  And [mathtype]

Or [mathtype]

Where [mathtype]

The nature of the roots of the equation depends upon the value of D, so it is called the discriminant.

Based on the value of the discriminant,[mathtype]  , the roots of a quadratic equation can be of three types.

Case 1: If D>0, the equation has two distinct real roots.

Case 2: If D=0, the equation has two equal real roots.

Case 3: If D<0, the equation has no real roots.

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