In recent times, it has become quite difficult for students to study strategically and earn their desired goals. Not having appropriate guidance is one of the key factors responsible for students lagging in their curriculum. One of the subjects which kids, in general, find difficult and boring is Maths. Solving math problems and equations already are challenging and to top it off, it is not utterly their favorite subject. It can be strenuous to prepare for a math exam altogether Quadratic equation is one such sub-part of Maths that can be quite difficult to crack if not understood aptly. Various online platforms offer classes and practice sessions for kids to understand the concepts.
Cuemath is an online learning platform that provides classes and worksheets for all your maths queries. It is quite practical and simple to use this website. All the worksheets are separated based on grades and topics, which makes it effortless and a time-saver to find what you are looking for.
What is a Quadratic formula and equation?
A general quadratic equation is:
, where a, b are the coefficients, x is the variable and c is constant.
A quadratic equation represents an equation of a second degree of x. Solving the equation gives us roots of the quadratic equation which in general, are the two values of x. These roots are represented as α, β.
Conditions for writing a quadratic equation:
- The coefficient of x i.e. ‘a’ should not be zero. If that happens then the term x2 will become non-existent and the equation will not be quadratic anymore.
- The numeric values i.e. ‘a’, ‘b’, ‘c’ should not be in terms of fractions or decimals. It should only be in integers.
- Sometimes, the equations are represented as (x-1) (x-2) = 5, 6(x2+5x) + 2=0. Although these are quadratic equations but not in standard form. The foremost step in solving a quadratic equation should be to write it in standard form.
What is Quadratic formula?
Sometimes the quadratic equations are complex and cannot be solved by using simple methods. This method is mainly used when the roots of the equation are complex. Substituting the values of a, b, c, further gives you two equations that can be solved separately. One of the equations will be formed with the positive sign and the other with the negative. Further, this quadratic formula helps to find the sum and product of the roots of the quadratic equation.
Discriminant of a quadratic equation:
The discriminant of a quadratic equation indicates the nature of the roots that assist us to decide the solving method of equations.
- If D>0 then, the roots are real and distinct
- If D=0 the, the roots are real and equal
- If D<0 then, the roots are imaginary
If the discriminant is negative, the equation is represented in complex numbers.
Methods to solve quadratic equations:
- Factorizing the quadratic equation
- Splitting the middle term into two numbers so that their sum is equal to the middle term and the product is the same as the constant.
- Forming factors by taking the common term out from the available term.
- Substituting both the factors as zero and finding the values of x.
- Formula method of finding roots
- Using the quadratic formula
- Completing the square
- Take the constant on the right side and divide the whole equation with the coefficient of x2
- Introduce the term ‘(b/2a) 2’ on both sides.
- Further, solve the new equation formed.
- Graphing method
- The graphing method makes it easy to solve a quadratic equation without the cumbersome calculations.
- Write the whole quadratic equation as,
- Further with the hit and trial method obtain the values of x, y and plot them on a graph
- The points where the parabola cuts the x-axis are the roots of the equation.
If your concept of quadratic equations is not clear, visit website of Cuemath. They have lucid methods to help understand the concept with the assistance of expert teachers.