Quadratic Equation Calculator
Online Quadratic Equation Calculator makes your quadratic equation calculation process easy and quick. Simply enter quadratic equation in the input box and hit on the calculate button to generate the output values.
Quadratic Equation Calculator: Are you checking for the best tool that computes the quadratic equation and gives the possible variable values? If yes, this is the right place for you. We are giving the easiest way to solve the quadratic equation using the formula or factors methods. Go through the below sections and check the manual procedure to compute the quadratic equation effortlessly. At this article, you will get both step by step procedure and online tool that gives accurate results in short span of time.
Steps to Solve Quadratic Equation Easily
Quadratic Equation is an equation having the highest power 2. Below listed are the simple guidelines that are helpful to you to solve any type of quadratic equation. Have a look at them and use them whenever required.
- Take any quadratic equation which is in the form of ax2 + bx + c = 0, where a≠0.
- Find out the a, b, and c values in your equation.
- To get the root values, you need to find out the discriminant value.
- Now, find the discriminant using the formula D=b2−4ac.
- After evaluating the D value substitute it in the below formula.
- The formula to find roots of the equation is x1 = -b - √D / 2a and x2 = -b + √D / 2a.
- Replace the values and perform arithmetic operatios to get the 2 roots.
Example
Question: Solve the quadratic equation x2 - 15x + 56 = 0 by using the quadratic formula?
Solution:
Given quadratic equation is x2 - 15x + 56 = 0
The standard form of quadratic equation us ax2 + bx + c = 0
In this case, a = 1, b = -15, c = 56
The formula to find the discriminant is D = b2 - 4ac
By substituting the above values:
D = (-15)2 - 4. 1. 56
= 225 - 224
= 1
The formula to find roots of equation is
x1 = -b - √D / 2a and x2 = -b + √D / 2a
x1 = -(-15) - √1 / 2.1
= 15 - 1 / 2 = 14/2 = 7
x2 = -(-15) + √1 / 2.1
= 15 + 1 / 2
= 16/2 = 8
x1 = 7, x2 = 8.
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FAQs on Quadratic Equation Calculator
1. What is the standard form of the quadratic equation?
The basic form to represent the quadratic equation is ax2 + bx + c = 0.
Here a, b, c are the constant values and x is a variable.
a should not be equal to zero.
2. What is the quadratic formula to find the square roots of the quadratic equation?
The formula to get the possible roots of quadratic equation is
x1 = (-b + √b2 - 4ac) / 2a
x2 = (-b - √b2 - 4ac) / 2a
b2 - 4ac is called discriminant which reveals the nature of the roots that equation has.
If discriminant = 0, the roots are equal, rational and real.
If discriminant ＞ 0, and also a perfect square, then roots are real, distinct and rational.
If discriminant ＜ 0, but not a perfect square, then roots are real, irrational and distinct.
3. What are the different methods to solve the quadratic equation?
The four different methods to solve any type of quadratic equation are listed here:
- Factoring: Find the factors of the given equation and those factors will be roots.
- Using the square root method: In this method b = 0. Convert the equation into the form x = √c/a to get the roots.
- Completing the squares
- Quadratic formula
4. How do you solve the quadratic equations using the Completing the squares method?
- Divide all terms by a (the coefficient of x2).
- Move the term c/a to the right side of the equation.
- Complete the square on the left side of the equation and balance this by adding the same value to the right side of the equation.
- Apply square root on both sides of equation.
- Subtract the number that remains on the left side of the equation.
5. Solve x2 - 14x + 45 = 0 by using the factoring method?
Given equation is x2 - 14x + 45 = 0
x2 - 9x - 5x + 45 = 0
x(x-9) - 5(x-9) = 0
(x-5)(x-9) = 0
x1 = 5
x2 = 9