Concept Used :-

Nature of roots :-

Let us consider a quadratic equation ax² + bx + c = 0, then nature of roots of quadratic equation depends upon Discriminant (D) of the quadratic equation.

• If Discriminant, D > 0, then roots of the equation are real and unequal.

• If Discriminant, D = 0, then roots of the equation are real and equal.

• If Discriminant, D < 0, then roots of the equation are unreal or complex or imaginary.

Where,

• Discriminant, D = b² - 4ac

Here,

The given quadratic equation is

On comparing with ax² + bx + c = 0, we get

Now,

Discriminant, of quadratic equation is given by

On substituting the values of a, b and c, we get

ADDITIONAL Information :-

A quadratic equation is an equation of degree 2, mean that the highest exponent of this equation is 2. Moreover, the STANDARD quadratic equation is ax² + bx + c, where a, b, and c are real numbers or arbitrary constants and ‘a’ cannot be 0. An example of quadratic equation is 2x² + 5x + 4.

The quadratic expression can also be written as:

• Standard FORM: y = ax² + bx + c, here a, b, and c are real numbers.

• Factored Form: y = (AX + c) (bx + d) here also a, b, and c are real numbers.

• Vertex Form: y = a (x + b)² + c, and here also a, b, and c are real numbers.