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Last updated date: 24th Jan 2023
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A quadratic equation solver, also known as quadratic formula solver, is a free online step-by-step quadratic solver tool that helps you to find the values of the variable by solving the given quadratic equation. With the help of this quartic equation solver, you can easily determine the roots of quadratic equations given by ax² + bx + c = 0, where the variable has two roots. The quadratic solver derives the solution using the quadratic formula given below:

$x={\frac{-b \pm\sqrt{b^{2}-4ac}}{2a} }$

In the above quadratic formula, the variables a, b, and c are real numbers and a 0. If a = 0, then the equation becomes linear and we call it a linear equation.

## What are the three Different Types of Quadratic Equations?

The three different types of quadratic equation are as follows:

• Factored Form

• Standard Form

• Vertex Form

In General, there are four different methods to solve the different types of quadratic equations mentioned above. The four different methods are:

• Factoring

• Using Square Root

• Completing The Squares

The quadratic formula solver given here enables you to solve the quadratic equation simply by using the quadratic formula.

## What is the Quadratic Formula?

An equation in the form of ax² + bx + c = 0, where a 0 is known as the quadratic equation.

$x={\frac{-b \pm\sqrt{b^{2}-4ac}}{2a} }$

The solution(s) to the quadratic equation can be calculated using the quadratic formula:

The () in the above quadratic formula means, there are normally two solutions.

The part (b² - 4ac) in the formula is known as “discriminant” because it can discriminate between the different possible answers.

• When the discriminant part is positive, we get two real solutions

• When the discriminant part is zero, we just get one solution.

• When the discriminant part is negative, we get no real solution.

## How to Use Quadratic Formula Solvers?

The procedure to use a quadratic equation calculator is given below:

• Enter the values of the coefficient such as a, b, and c in the respective input field.

• Now click on the button “ Calculate Quadratic Equation” to get the roots.

• At last, the roots of the given quadratic equation and the discriminant will be displayed in the output field.

Enter the coefficient values a, b, and c in the quadratic solver given below to solve any of the given quadratic equations.

Quadratic Equations: ax² + bx + c

Enter the value of coefficient ‘a’ :

Enter the value of coefficient ‘b’ :

Enter the value of coefficient ‘c’ :

Discriminant D:

Value of x₁:

Value of x₂:

Here, x₁ and x₂ are root 1 and root 2.

Note: If inputs are entered precisely in the preceding quadratic equation calculator, it will display the solution of the given quadratic equation in a fraction of a second.

## What are the Benefits of Using Quadratic Formula Calculators?

Following are the benefits users can explore while using a quadratic formula calculator:

• The calculator helps you to solve the given quadratic problem without depending on your teacher or friend even if you get stuck at some step.

• This calculator enables you to complete your assignments or homework on time.

• Once you enter the input and press the “Calculate Quadratic Equation” button, the calculator will provide you with a stepwise explanation of the problem. Along with getting an accurate answer, you will also learn how the equation is solved.

• The quadratic equation solver given here helps you to solve all types of quadratic equations, either in factored form, standard form, or vertex form in a fraction of seconds.

• The most important part of the quadratic equation solver given here is that it is available free of cost and is available in all types of window versions or browsers.

## Solved Examples

1. Find the roots of $x^{2} +4x +5 = 0$, if any exist, using the quadratic formula.

Solution:

Given Quadratic equation is $x^{2} +4x +5 = 0$

To check whether there are real roots available for the quadratic equation, we need to find the discriminant value.

$D= b^{2}-4ac = (4^{2})-4(1)(5) =16-20= -4$

Here the square root of - 4 will not give a real number. Hence there are no real roots for the given equation.

2. Find the roots of the equation $2x^{2} -5x +3 = 0$ using factorisation.

Solution:

Given, equation is $2x^{2} -5x +3 = 0$ = 0

$2x^{2} -5x +3 = 0$ = 0

2x(x-1)-3(x-1) = 0

(2x-3) (x-1) = 0

So,

2x-3 = 0; x = $\dfrac{3}{2}$

(x-1) = 0; x=1

Therefore,$\dfrac{3}{2}$ and 1 are the roots of the given equation.

3. Solve the quadratic equation $2x^{2} -x -28 = 0$ using the quadratic formula.

Solution:

If we compare it with standard equation,$ax^{2} +bx +c = 0$

a=2, b=1 and c=-28

Hence, by using the quadratic formula:

$x={\frac{-b \pm\sqrt{b^{2}-4ac}}{2a} }$

Now let us substitute the respective value in the above formula

$x={\frac{-b \pm\sqrt{b^{2}-4ac}}{2a} }$

$x={\frac{-1 \pm\sqrt{(-1)^{2}-4(2)(-28)}}{2\times 2} }$

$x= \frac{-1\pm \sqrt{1+224}}{4}$

$x= \frac{-1\pm \sqrt{225}}{4}$

$x= \frac{-1 \pm 15}{4}$

$x= \frac{-1 + 15}{4}~~~~~or~~~~ x= \frac{-1-15}{4}$

$x= \frac{14}{4}~~~~~or~~~~ x= \frac{-16}{4}$

$x= \frac{7}{2}~~~~~or~~~~ x= -4$

### Practise Questions

1. Find the roots of the given quadratic equation i.e, $x^{2} -15 +56 = 0$

a) x = 14 or x = 4

b) x = 8 or x = 7

c) x = 28 or x = 2

d) All of the above

2. In the given equation for what value of k does the equation $x^{2} -12x +k = 0$ have real and equal roots?

a) 61

b) 35

c) 67

d) 36

3. Find the discriminant of the equation: $3^{2} -2x +\dfrac{1}{3} = 0$.

a) 1

b) 2

c) 3

d) 0

1) b

2) d

3) d

## Conclusion

Competitive Exams after 12th Science

## FAQs on Quadratic Equation Solver

A quadratic equation is a second order equation written in the form of ax² + bx + c = 0,  where a, b, and c are coefficients of real numbers, and the coefficient 'a' is not equal to zero.

2. Who Introduced the Quadratic Formula?

The quadratic formula covering all the cases was first introduced in 1594 by Simon Stevin. In 1963, Rene Descartes published La Geometrie and introduced the quadratic formula in the form we know at present.

3. Mention a Few Real-life Applications of Quadratic Equations?

Many real-world applications deal with quadratic functions such as diving from a platform, shooting a cannon, throwing a ball, and hitting a ball are all examples of a quadratic function.

4. What is the Use of the Roots of a Quadratic Equation Solver?

The roots of a quadratic equation solver is an online tool used for calculating the roots of quadratic equations.

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