# Discriminant

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Discriminant is an expression that is used to determine the properties of an equation.  The Discriminant of an equation gives the number of roots and nature of roots.  In quadratic equation ax^2 + b x+ c =0, the discriminant is b^2 – 4ac. This discriminant is used to find out number and nature of roots of quadratic equation.

More on Discriminant

If discriminant = 0 then equation has one real root.

If discriminant > 0, then the equation has 2 real roots.

If discriminant < 0, then the equation has two imaginary roots.

Problem 1: Find out the number of solutions of the equation by using its discriminant. Check whether the solutions are real or imaginary.  3x^2 + 12 x + 12 = 0

Solution: Given equation is 3x^2 + 12 x + 12 = 0

=> Now compare the equation with standard form ax^2 + b x + c= 0

=> The value of a = 3, b = 12 and c=12

=> We know Discriminant is b^2 - 4ac

=> Substitute the values: b^2 - 4ac = 12^2 – 4(3)(12) = 0

=> Since the Discriminant = 0 the equation has one real solution.

Problem 2: Find out the nature of roots of the Quadratic equation 2x^2 – 5x – 12 = 0 by using its discriminant.
Solution: Given equation is 2x^2 – 5x – 12 = 0

=> Now compare the given equation with standard form ax^2 + b x + c= 0

=> The value of a = 2, b = -5 and c= -12

=> Discriminant = b^2 - 4ac = (-5) ^ 2 – 4 (2) (-12) = 121

=> Since, Discriminant = 121 > 0.

=> Therefore the roots are real and unequal.