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SAI International School
CLASS - X

Mathematics
CHAPTER-4: Quadratic Equations, -5

Lesson Notes- 5

Sub Topic: Nature of roots

Solution or root of Quadratic Equation
The values of x for which a quadratic equation is satisfied are called the roots or
solutions of the quadratic equation.

As quadratic polynomials have degree 2, therefore Quadratic Equations can have two
roots.
Graph of a quadratic polynomial is a parabola.

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For a quadratic polynomial ax +bx+c,
If a>0, the parabola opens upwards.
If a<0, the parabola opens downwards.
If a = 0, the polynomial will become a first-degree polynomial and its graph is linear.
Nature of Roots

From the quadratic formula, we can see that the two roots of the Quadratic Equation are
given by:

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Where D = b – 4ac
The nature of the roots of the equation depends upon the value of D, so it is called
the discriminant.

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