The quadratic formula is one of the three main ways to find the roots of a second-degree polynomial equation, others are completing square and breaking into factors. Quadratic formula is
x = \(\dfrac{-b \pm \sqrt{b^2 - 4ac}}{2\left(a\right)}\)
Where "\(b^2 - 4ac\)" is also called the discriminant of the equation represented by delta.
A second-degree polynomial equation is one in which the highest power of variable (e.g x) is 2. For example, \(4x^2-22x = x^2+5, -2x^2+x+5=0, -2x^2+15=x^2-12\). For the implication of the quadratic formula on the quadratic equation, the equation must be solved to \(ax^2+bx+c=0\) form. For instance, let an equation be \(5x^2-10x+1=x+4\). if we want to find the roots through the quadratic formula, we will have to get one coefficient for one distinct power of the variable i.e. \(5x^2-11x-3=0\).
Discriminant provides important information about the roots of the equation.
When coefficients a,b and c are real numbers and have no imaginary part i.e i. Also \(a \neq 0\). E.g consider a quadratic equation \(x^2+5x + 6\). if we solve it through quadratic formula, the steps are following
Roots having an imaginary number in them. The simplest imaginary number is \(i = -1\). Such roots do have real numbers in them but due to the presence of i, the whole root is called imaginary. E.g let us solve the equation \(x^2-5x +7\).
The real numbers along with the variable in an equation are called coefficients of a quadratic equation. Coefficients are not dependent on the variable such as x, y, and z. It is not essential that only x can be the variable. We can use any alphabet as a variable. Only one type of variable is present in a quadratic equation. It is not possible for a quadratic equation to have more than one variable. If there is no coefficient written with “x”, it means its coefficient is 1. If its second-degree polynomial and coefficient of x2is zero, It’s not a quadratic equation, it is a linear equation.
The quadratic formula is obtained by completing the square method.
The quadratic formula is one of the easiest ways to solve a quadratic equation. You can solve a quadratic equation as instructed.
As you can see from the procedure written above for solving the quadratic equation, this work can take a great deal of your time. Why not use a quadratic equation solver which will not only give you answers but also tell you the procedure, nature of roots and give you a plotted graph. Seems impossible? But not for us. Yes! By using our quadratic formula calculator you will not only get the answers but also previously mentioned things. You’ll need to follow only one step to get your answer and that step is
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