How to solve Quadratic Equations

Quadratic equations are very easy to solve using a calculator. Alcula’s  scientific calculator makes it even easier. This is the first of a series of examples of how entering commonly used formulas as user defined functions into the  scientific calculator can help you streamline your work, weather your are checking your homework or verifying the solutions to the exercises in your math textbook.

What are quadratic equations?

A quadratic equation is an equation that is represented in general form:

Quadratic Equation

a,b and c are constants:  a is the quadratic coefficient, b the linear coefficient and c is the constant term.

The quadratic equation formula

Quadratic equations are very easy to solve if you know the simple formulas:

Quadratic Formulas

The  b2minus4ac portion of the formula is called the ‘discriminant‘.

When the discriminant is less than 0, the quadratic equation has no real solutions (because the square root of a negative number is not real).

If the discriminant is 0, it has 1 real solution.

It it is greater than 0 it has two real solutions.

Entering the formulas in the calculator

Simply enter the two formulas as functions in the calculator window:




(You can copy and paste them)

Now try it with a few quadratic equations…

Solving quadratic equations with the scientific calculator

Now that you have entered the functions it’s very quick to solve any quadratic equation like the following:




Simply enter f(1,5,6) and g(1,5,6) to find the results for the first one, f(2,3,3) and g(2,3,3) for the second, and f(1,0,4) and g(1,0,4) for the third.

Solving quadratic equations on the calculator

Solving quadratic equations on the calculator

Note that the last two equations have no real solutions.

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