How To Solve An Equation By Using The Quadratic Formula How To Tell The Nature Of Roots Of Quadratic Equations!

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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. Once they are solved, we get the solution as the two values ​​of the variable in them. Solutions have many names, such as roots, zeros, and variable value. The key is that the variable has two values ​​and they can be real and imaginary. Tenth through twelfth graders must know both types of solutions (roots). In this presentation I will focus only on the actual roots.

There are three possibilities for the roots of an equation of two degrees. Since these equations have degree two, the variable they contain will have two values, but this is not always the case.

Sometimes there are two roots that are distinct and unique, sometimes the equation has both the same roots, and sometimes the equation has no solution. The absence of a solution to an equation means that there is no such way of solving the equation to obtain the real value (real roots) of the equation, and these types of equations can have imaginary roots.

There is a method for telling the nature of the roots of quadratic equations without solving the equation. This method involves finding the value of the discriminant (symbol D) of a quadratic equation.

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

D = b² – 4ac

Where “D” represents the discriminator, “b” is the coefficient of the linear term, “a” is the coefficient of the quadratic term (the term with the square of the variable), and “c” is the constant term.

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

1. If D > 0

In this case, the equation has two different real roots.

2. If D = 0

In this case, the equation has two equal roots.

3. If D < 0

In this case, the equation has no real roots.

For example; suppose we want to know the nature of the roots of the 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 for 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, the discriminant is the key to predicting the nature of quadratic equations. Once the value of the discriminant is calculated using this formula, the nature of the roots of the quadratic equation can be predicted.

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