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## Quadratic Formula Calculator

## Calculator Use

This online calculator is a

quadratic equation solver that will solve a second-order polynomial equation such as ax2 + bx + c = 0 for x, where a ≠ 0, using the

quadratic formula.

The calculator solution will show work using the quadratic formula to solve the entered equation for real and complex roots. Calculator determines whether the discriminant \( (b^2 – 4ac) \) is less than, greater than or equal to 0.

When \( b^2 – 4ac = 0 \) there is one real root.

When \( b^2 – 4ac > 0 \) there are two real roots.

When \( b^2 – 4ac < 0 \) there are two complex roots.

## Quadratic Formula:

The quadratic formula

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

is used to solve quadratic equations where a ≠ 0 (polynomials with an order of 2)

\( ax^2 + bx + c = 0 \)

Examples using the quadratic formula

Example 1: Find the Solution for \( x^2 + -8x + 5 = 0 \), where a = 1, b = -8 and c = 5, using the Quadratic Formula.

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

\( x = \dfrac{ -(-8) \pm \sqrt{(-8)^2 – 4(1)(5)}}{ 2(1) } \)

\( x = \dfrac{ 8 \pm \sqrt{64 – 20}}{ 2 } \)

\( x = \dfrac{ 8 \pm \sqrt{44}}{ 2 } \)

The discriminant \( b^2 – 4ac > 0 \) so, there are two real roots.

Simplify the Radical:

\( x = \dfrac{ 8 \pm 2\sqrt{11}\, }{ 2 } \)

\( x = \dfrac{ 8 }{ 2 } \pm \dfrac{2\sqrt{11}\, }{ 2 } \)

Simplify fractions and/or signs:

\( x = 4 \pm \sqrt{11}\, \)

which becomes

\( x = 7.31662 \)

\( x = 0.683375 \)

Example 2: Find the Solution for \( 5x^2 + 20x + 32 = 0 \), where a = 5, b = 20 and c = 32, using the Quadratic Formula.

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

\( x = \dfrac{ -20 \pm \sqrt{20^2 – 4(5)(32)}}{ 2(5) } \)

\( x = \dfrac{ -20 \pm \sqrt{400 – 640}}{ 10 } \)

\( x = \dfrac{ -20 \pm \sqrt{-240}}{ 10 } \)

The discriminant \( b^2 – 4ac

Simplify the Radical:

\( x = \dfrac{ -20 \pm 4\sqrt{15}\, i}{ 10 } \)

\( x = \dfrac{ -20 }{ 10 } \pm \dfrac{4\sqrt{15}\, i}{ 10 } \)

Simplify fractions and/or signs:

\( x = -2 \pm \dfrac{ 2\sqrt{15}\, i}{ 5 } \)

which becomes

\( x = -2 + 1.54919 \, i \)

\( x = -2 – 1.54919 \, i \)

calculator updated to include full solution for real and complex roots

Aptitude Questions: Quadratic Equations Set 12 – Follow the link To solve Quadratic Equations with the help of Number Line. x2 – 11x + 24 = 0, y2 + 9y + 18 = 0. TAGS. Quadratic Equations Quiz. Previous articleEnglish Questions: Antonyms – 10.This one is not a quadratic equation: it is missing x2 (in other words a=0, which means it can't be quadratic). Have a Play With It. The "solutions" to the Quadratic Equation are where it is equal to zero. They are also called "roots", or sometimes "zeros". There are usually 2 solutions (as shown in…Solve linear or quadratic inequalities with our free step-by-step algebra calculator. Since each equation obtained in the process is equivalent to the original equation, -3 is also a solution of 2x + 1 = x – 2. In the above example, we can check the solution by substituting – 3 for x in the original…

Quadratic Equations – a=2 A general standard quadratic equation is in the form ax^2+bx+c=0, where a is the coefficient of term x^2 b is the coefficient of term x and c is the constant term In the given equation 2x^2+11x+10=0, as the coefficient of x^2 is 2, a=2. Algebra Quadratic Equations and Functions Quadratic Formula.Sal determines how many solutions the equation x²+14x+49=0 has by considering its quadratic formula, and more specifically, its discriminant.Roots of Quadratic Equations and the Quadratic Formula. In this section, we will learn how to find the root(s) of a quadratic equation. If the discriminant of a quadratic function is equal to zero, that function has exactly one real root and crosses the x-axis at a single point. f(x) = 2×2− 11x + 5.

Solve inequalities with Step-by-Step Math Problem Solver – Free Online Equation Calculator helps you to solve linear, quadratic and polynomial systems of equations. Answers, graphs, alternate forms. Wolfram|Alpha is a great tool for finding polynomial roots and solving systems of equations. It also factors polynomials, plots polynomial solution sets and…leisleyhenry leisleyhenry. u2 – 11u + 24 = 0 where u = (x2 – 1) the first awnser, a. substitute the value of u in the equation.Class 10 Mathematics Notes – Chapter 1 – Quadratic Equation – Exercise 1.2. Notes that contain all the important questions of the exercise.