One of the most scoring subjects included in the curriculum of CBSE class 10 is Mathematics, as many students fetch a full mark in this subject. With the least number of definitions to be learned in the syllabus, Mathematics is a practice subject. Once the theorems and laws the topics are done at school, students only need to practice the sums over and over again, so as to achieve a full score. A good score in Mathematics happens to be highly beneficial for the class 10 results, as it hikes a student’s aggregate percentage.
The quadratic equation class 10 NCERT is one of the most important concepts that students need to have a good understanding of. A standard quadratic equation included in the syllabus of CBSE class 10 mathematics is of the form ax2+ bx + c = 0. Since variable x is raised to the power of 2, this standard form of a quadratic equation is also referred to as the equation of degree 2. Let us understand what each of these terms in the quadratic equation stands for.
ax2+ bx + c = 0
The purpose of solving this type of quadratic equation is to find the roots or values of x that will satisfy the given quadratic equation. ax2, bx, and c are generally referred to as the terms of the quadratic equation. Hence, in a standard form of quadratic equation, there are a total of three terms.
In the above-mentioned equation, xis a variable and a, b, and c are constant values. For solving the sums of quadratic equations, students must have a clear understanding of the concept of ‘Factorization’.
How to solve a quadratic equation?
Two methods of solving a quadratic equation are explained in the vedantu ncert solutions for class 10 maths chapter 4. One of the methods requires students to factorize the terms in the equation while the other method implements a formula, to find the roots of the quadratic equation. At times it is mentioned in the question itself, which of the two ways is to be followed while solving for the given quadratic equation. The methods are discussed briefly below.
Sometimes, there are hidden quadratic equations in the sums of quadratic equation class 10. The given quadratic equation has to be so solved that there happens to be three terms as ax2, bx and c in the equation.
- The values of ‘c’ and ‘a’ are multiplied along with their respective signs.
- The product so obtained is factored into two terms. The factors of the product of ‘a’ and ‘c’ have to be chosen, so that they result in a value equal to ‘bx’.
- The next step is to group the four terms in the following order : (x+m)(x-n).
- In the following or last step, each of these terms (x+m) and (x-n) have to be equated to zero.
=> x = -m
(x-n) = 0
=> x = n
- Therefore, the roots of the given quadratic equation are -m and +n. Students can refer to the ncert solutions for class 10 maths chapter 4 for a better understanding of this concept.
This method implements a formula,
x= -b + (b2-4ac)2a
Students are required to substitute the values of a, b and c in the above-mentioned formula as per the given equation. The two roots of the quadratic equation becomes,
x= -b +(b2 – 4ac)2a and x= -b -(b2 – 4ac)2a
The term (b2 – 4ac) is referred to as the Discriminant. It can be used to determine if the roots of a quadratic equation are real, equal or imaginary. The sums of quadratic equation class 10 will help students to have a clear idea of the implementation of this formula.
|Real Roots||Equal Roots||Imaginary Roots|
|If (b2 – 4ac)> 0,then the roots of the given quadratic equation are called real roots.||If (b2 – 4ac)= 0,then the roots of the given quadratic equation are called equal roots.||If (b2 – 4ac)< 0,then the roots of the given quadratic equation are called imaginary roots.|
Some interesting things to remember while solving any quadratic equation are listed below.
- While the values of b and c in any quadratic equation can be 0 but the value of a can never be equal to 0.
- While solving quadratic equations, there happens to be an intermediate step in the sum, wherein four terms are there on the L.H.S. (left hand side) of the equation. It can be determined if the sum is correct or not, by scrutinizing this intermediate step. Out of the four terms in this step, two of the terms are supposed to have a positive sign while the rest of the two terms are supposed to have a negative sign. A correct solution of any quadratic equation cannot have any different case in this intermediate step.
- Any quadratic equation in the ncert solutions for class 10 maths chapter 4, has two roots or values of x.
- Students can solve quadratic equations and check if the answers are correct, by substituting the values of xin the given quadratic equation. If the resultant values on the ‘L.H.S’ (left hand side) and the ‘R.H.S.’ are equal, then the answers are correct.
Among the other important chapters for class 10 maths board exam, linear equations in two variables and mensuration carry a greater weightage of marks. The initial sums of these chapters are pretty easy to solve but some of the difficult sums have applications of quadratic equations as well. Students must be thoroughly familiar with the concept of quadratic equations since hidden quadratic equations are likely to be there in those sums.
While solving the sums of linear equations in two variables and mensuration, students may have to frame quadratic equations in the intermediate steps. For example, they may need to solve a quadratic equation while finding the value of some dimensions of 3D figures. Hence, students are suggested to practice all the sums of quadratic equations from the NCERT maths textbooks, prescribed maths reference books and the previous years question papers.