The beauty of numerical problems in mathematics is that the same problem can be solved by different people in completely different ways with the identical results. However, some methods are always easier and quicker as compared to others. There are mathematical equations to express different types of curve. A line is the simplest curve expressed in the form of a linear equation. In a linear equation, the maximum power over variables is one. For more complex curves we have equations with more terms consisting of a higher power of the variable. A quadratic equation is equation with one variable such that it contains a term with a variable having power 2 and there are no other terms with the higher power of the variable. In general, we express a quadratic equation as: ax^2 + bx + c = 0. Here a, b and c are constants and x is the variable. a cannot be zero as it will make the term ax^2 as 0.
A quadratic equation consists of two solutions or roots for the variable x. Roots of an equation simply mean that for these two values of the variable, the equation will become zero. There are several ways to calculate the roots of a quadratic equation such as graphical method, factoring etc but quadratic formula is the easiest and the simplest way to find the roots of any quadratic equation. So, the things we need to know is ‘What is Quadratic Formula’ and how can we use it to solve a quadratic equation.
What is Quadratic Formula
According to the quadratic formula, the two values of the variable x for a given quadratic equation-
ax^2 + bx + c = 0,
are given by:
Suppose the two values or roots of x are x1 and x2, then they are calculated by once taking the sign + and once – in the numerator of the quadratic formula.
The values of the variables a, b and c are to be determined for the given equation and they can be positive as well as negative. Also you would need to first write the equation is standard form with all the terms on one side and zero on the other side. Now that you know ‘What is Quadratic Formula’, let us take an example to implement it.
Suppose we have a quadratic equation,
4x^2 - 16x =-15,
We would first need to convert it into standard for as:
4x^2 - 16x + 15 = 0
Now, comparing it with the standard quadratic equation, ax2 + bx + c = 0; we can write,
a = 4, b = -16 and c = 15.
So, according to quadratic formula, the two roots of this quadratic equation are:
x1 = =
x2 = =
Note: In the quadratic formula b^2 means square of b and not 2 multiplied by b. Also, the square root in the numerator is calculated for the complete term b2 – 4ac and not just b2.
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