Nature of Roots

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

[mathtype]x = \dfrac{{ - b + \sqrt {{b^2} - 4ac} }}{{2a}}  And [mathtype]\dfrac{{ - b - \sqrt {{b^2} - 4ac} }}{{2a}}

Or [mathtype]x = \dfrac{{ - b \pm \sqrt D }}{{2a}}

Where [mathtype]D = {b^2} - 4ac

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]D = {b^2} - 4ac  , 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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