AdBlocker Detected
adblocker detected
Calculatored depends on revenue from ads impressions to survive. If you find calculatored valuable, please consider disabling your ad blocker or pausing adblock for calculatored.
ADVERTISEMENT
ADVERTISEMENT

Quadratic Formula Calculator

ADVERTISEMENT
ADVERTISEMENT

The quadratic formula calculator helps you to find the roots of the quadratic equation and shows step-by-step calculations. Our free online tool gives explicit results by optimizing the use of resources.

Quadratic Formula:

The Latin word “quadratic” comes from quadratum, generally used for square.

Our quadratic equation solver helps you to reduce the following second-degree expression to its roots:

$$ ax^2 + bx + c = 0 $$

Where,

  • x is the unknown value
  • a, b is the quadratic coefficient, a ≠ 0
  • c is a constant

Derivation of Quadratic Formula:

$$ \dfrac{a}{a}x^2 + \dfrac{b}{a}x + \dfrac{c}{a} = 0 $$

$$ x^2 + \dfrac{b}{a}x + \dfrac{c}{a} = 0 $$

$$ x^2 + \dfrac{b}{a}x = -\dfrac{c}{a} $$

Add $$ (\frac{b}{2a})^2 $$ on both sides of the equation.

$$ x^2 + \dfrac{b}{a}x + (\dfrac{b}{2a})^2 = -\dfrac{c}{a} + (\dfrac{b}{2a})^2 $$

$$ (x + \dfrac{b}{2a})^2 = -\dfrac{c}{a} + \dfrac{b^2}{4a^2} $$

$$ (x + \dfrac{b}{2a})^2 = \dfrac{b^2 – 4ac}{4a^2} $$

Take a square root on both sides of the equation.

$$ \sqrt{(x + \dfrac{b}{2a})^2} = \pm \sqrt{\dfrac{b^2 – 4ac}{4a^2}} $$

$$ x + \dfrac{b}{2a} = \pm \dfrac{\sqrt{b^2 – 4ac}}{2a} $$

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

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

How To Use Quadratic Formula?

The quadratic formula calculator helps you to solve any quadratic equation in a matter of seconds. However, if your goal comes up with the manual calculations, you must delve into the example to explore more.

Example:

Suppose that we have 3x^2 - 5x + 2 = 0. We need to solve by the quadratic equation formula.

Solution:

We already know about the formula that is:

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

And we also know the values of a, b, and c in the above-given statement:

a= 3, b= -5, and c= 2

Put the values in the formula. 

$$ x = \dfrac{-5 \pm \sqrt{-5^2 – 4(3)(2)}}{2(3)} $$

$$ x = \dfrac{5 \pm \sqrt{25 – 24)}}{6} $$

$$ x = \dfrac{5 \pm \sqrt{1}}{6} $$

Here the roots of a quadratic equation have two solutions. 

Root # 1

$$ x = \dfrac{5+1}{6} $$

$$ x =\dfrac{6}{6} $$

$$ x = 1 $$

Root # 2

$$ x = \dfrac{5-1}{6} $$

$$ x = \dfrac{4}{6} $$

$$ x = \dfrac{2}{3} $$

To learn more about quadratic equations and their calculations, find our complete quadratic tutorial for free.

Working of Quadratic Formula Calculator:

The quadratic root calculator will help you carry out calculations easily! Just enter the required values. Our quadratic function calculator will work best for you! 

Input:

  • Choose equation form
  • Choose computation method
  • Put the values of a, b, and c in the respective field
  • Press the “Calculate” button

Output:

  • Quadratic formula solver will give you an instant answer with the steps and graph shown

FAQs:

How Many Possibilities Does a Quadratic Equation Have?

There are three possibilities which include:

  • If the discriminant is positive, then there are 2 solutions 
  • If the discriminant is negative, then there is no solution 
  • If the discriminant equals 0, then there is 1 solution 

Can a Quadratic Formula be Used for Everything?

No, It is just used to solve the quadratic equations that are in the form of $$ ax^2 + bx + c = 0 $$. This form is also known as the standard form of the quadratic formula calculator.

How Many Roots Does a Quadratic Formula Equation Have?

A second-degree equation formula equation has two roots. It depends on the degree of the equation.

References:

From the source Wikipedia: Quadratic equation, Solving the quadratic equation, Examples, and applications, History, Advanced topics

From the source Khan Academy: understanding quadratic formula, Example