A quadratic equation is a polynomial equation where the highest power attached to a variable is of order 2. As the highest power of the variable attached to the polynomial equation is two, it means that at least one term in the equation exists, which is squared. Because of this, the equation is called “quad”.
A quadratic equation can be expressed in the general form of ax2+bx+c=0, where a, b and c are numerical coefficients or constants, and the value of x is variable. One fundamental rule of a quadratic equation is that the value of the first constant never can be zero.
These equations make up a significant part that is necessary to solve several kinds of complicated mathematical problems. The practical use of quadratic equations is extensively seen while calculating the dimensions of parabola, the speed, and other dimensions of projectile motion involving athletics and sports.
Solutions of a Quadratic Equation
There are two fundamental methods to find the roots of a quadratic equation. They are
According to the Standard equation method, the roots of a quadratic equation can be found by the
x = [frac{-b pm sqrt{b^{2} – 4(a)(c)}}{2a}]
This equation is also known as the Sridharacharya Formula.
While in the Factorisation method, the constant “b” is broken down into such quantities so that the entire equation becomes a perfect factor where x can be taken as the common factor in ax2+bx.
Basic Concepts
There are several ways in which you can calculate quadratic equations. However, two of them are the most useful and accessible.
Standard Equation
Using this method, you can solve any quadratic equation. Suppose the equation is ax² + bx + c = 0, hence the value of x will be x = [frac{-b pm sqrt{b^{2} – 4(a)(c)}}{2a}]
It is also known as the Sridharacharya formula.
Employing this technique, you will get two types of value. One of these will be positive, and the other one will be negative.
Factorising Method
This method is in quadratic equation class 10 syllabus and therefore essential for you to learn about this in detail.
In this method, you obtain the solution factoring quadratic equation terms. However, for this, the equation has to be eligible for factoring. This technique is easier than others.
Consider this example of a quadratic equation and find the solution.
x² -5x + 6 = 0
The equation is the standard form quadratic equation. To find the solution of it, first you have to consider two terms that are b and c. In this case, b = -5 and c = 6. Now you have to find the product of which two numbers will be 6. Also, the sum of the two numbers has to be -5.
For that, find the factors of 6, which can be 1, 2, 3, and 6. Thereby, you will see that the product of 2 and 3 is 6 whereas the sum of 2 and 3 is 5. Since we have to find -5, we have to take -2 and -3, only then the sum will be -5 and the product will be 6.
Therefore, two factors of the equation are (x + 2) and (x + 3).
Quadratic Equation Problems
Following is the quadratic equation with solution
3x2 – x = 10
3x2 – x – 10 = 0
3x2 – 6x + 5x – 10 = 0
3x (x – 2) + 5 (x – 2) =0
(x – 2)(3x + 5) = 0
Therefore, x – 2 = 0, x = 2
And when 3x + 5 = 0; 3x = -5 or; x = -5/3
Thus, x= -5/3, 2
Conclusion
If you want to solve quadratic equations online, tune in to our website. Along with the notes, you can get access to the quadratic equation NCERT solution for grade 10.