Polynomials are one of those topics of mathematics that are taught to the students of primary classes. It is one of the topics basic concepts of mathematics without mathematics is incomplete. Students study different types of polynomials and their degrees in primary classes. A polynomial is an algebraic expression that consists of a minimum of two terms and the polynomial, which consists of two terms, is known as the Quadratic equation. Solving and the application of this equation is taught to students in higher classes.
A quadratic function is a type of polynomial function with more than one variable in which the highest degree or the power of the variable is two. Since the term with a maximum degree in a quadratic equation is two, therefore it is also termed the polynomial of degree 2. A quadratic equation has at least one term, which is of the second degree. They have scope in different fields of engineering and science to obtain values of various parameters. If represented on a graph sheet, they are represented by a curve parabola. The direction of the curve is decided based on coefficients of the highest degree of the equation.
f(x)=a(x-h)^2+k is the standard form of the quadratic equation. Here h and k are x and y Coordinate of vertex of the parabola, respectively. The value of ‘a’ is used to decide the path and direction of the curve. After simplifying the standard form, one can find the quadratic equation as f(x) = ax^2 + bx + c, which is the common and widely used form of Quadratic Equation.
The domain of the Quadratic equation is defined of all the real numbers so that it can be said as R. On the other hand, the range of the this function depends upon the side where the graph of the curve is open. Let’s discuss one of the most important and widely used formulas of mathematics, the Quadratic formula. This is also known as the Sridhar Acharya formula.
It is one of the simplest ways to find out the root of the quadratic equations. One can find the sum and the product of the roots of the equation with the help of the quadratic formula.
It is given as follows:
[-b ± √(b² – 4ac)]/2a
Here a, b, c are the coefficients of the quadratic equations.
The discriminant of the Quadratic equation is equal to D = b^2 – 4ac. This helps in finding out the nature of the roots.
- D is more than 0, then roots are real and different from one another.
- D is less than 0, then the roots of the equation don’t exist or can be termed imaginary.
- The last condition is when D=0, then the roots of the equation are real and equal to each other.
- One of the ways is by factorization of the equation.
- The second method is directly applying the Quadratic formula of finding roots.
- The third method to find the root is done by completing the square.
- Last is the graphical method to find the roots.
These are some of the ways to find out the roots of the quadratic equation.
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