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## How To Tell The Nature Of Roots Of Quadratic Equations!

**The nature of the roots of quadratic equations**

Quadratic equations are quadratic equations. When these are solved we get a solution in the form of two variable values. Solutions have many names, such as roots, roots and values of variables. The key has two variable values and they can be real and imaginary. In grades ten through twelve, math students should know both types of solutions (roots). In this presentation I focus only on real roots.

There are three possibilities regarding the roots of two degree equations. As the degrees of these two equations, they have two values of the variable contained in them, but this is not always the case.

Sometimes there are two distinct and unique roots, sometimes the equation has the same root and in some cases there is no solution to the equation. No solution to an equation means that there is no way to solve the equation to find the real value (real roots) of the equation and there may be imaginary roots in this class of equations.

There is a way to determine the form of the roots of a quadratic equation without solving the equation. This method involves finding the discriminant value (D as the characteristic) of the quadratic equation.

The formula to find the discriminant (D) is given below:

D = b² – 4ac

Where “D” stands for discriminant, “b” is the coefficient of the linear term, “a” is the coefficient of the quadratic term (the term with the square of the transformation) and “c” is the constant term.

The discriminant is calculated using the above formula and the result is analyzed as given below:

1. When D > 0

In this case there are two distinct real roots of the equation.

2. When D = 0

In this case there are two equal roots of the equation.

3. When D < 0

In this case there are no real roots of the equation.

For example; suppose we want to know the form of the roots of a quadratic equation, “3x² – 5x + 3 = 0”

In this quadratic equation; a = 3, b = – 5 and c = 3. Use these values in the formula to find the discriminant of the given equation as shown below:

D = b² – 4ac

= (- 5)² – 4 (3) (3)

= 25 – 36

= – 11 < 0

Hence, D < 0 and the given equation has no real roots.

Finally, it can be said that discrimination is the key to predicting the nature of quadratic equations. Once the discriminant value is calculated using its formula the root of the quadratic equation can be estimated.

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