Quadratic equation Class 10 Maths NCERT Solutions Chapter 4 is concerned with understanding quadratic equations and numerous methods for determining their roots. Students preparing for class 10 maths chapter 4 will be able to clear all their concepts on linear equations at the root level. Expert faculty of Toppr produced these solutions to assist students with their first term exam preparations. It covers all major concepts in detail, allowing students to understand the ideas better.
NCERT Solutions for class 10 maths chapter 4 of the section, concentrates on the essential concepts such as the quadratic equation definition, standard form of a quadratic equation, nature of roots, concept of discriminants, quadratic formula, factorization technique of solving a quadratic equation, and completing the square method. All of these solutions are designed with the new CBSE pattern in mind, so that students have a complete understanding of their tests.
Quadratic equation class 10 solutions are very useful for getting good grades in tests and properly preparing you with all of the important concepts. These NCERT Solutions are valuable tools that can assist you not only in covering the full syllabus but also in providing an in-depth analysis of the subjects. The Class 10 Maths NCERT Solutions Chapter 4 are available in pdf format below, and some of them are also included in the exercises.
Let $x$ be the base of the triangle, then the altitude will be $(x−7)$.
By Pythagoras theorem,
$x_{2}+(x−7)_{2}=(13)_{2}$
$2x_{2}−14x+49−169=0$
$2x_{2}−14x−120=0$
$x_{2}−7x−60=0$
$x_{2}−12x+5x−60=0$
$(x−12)(x+5)=0$
$x=12,x=−5$
Since the side of the triangle cannot be negative, so the base of the triangle is $12cm$ and the altitude of the triangle will be $12−7=5cm$.
A quadratic equation in the variable x is an equation of the form ax^{2} + bx + c = 0, where a, b, c are real numbers, a ≠ 0. In fact, any equation of the form p(x) = 0, where p(x) is a polynomial of degree 2, having a single variable, is a quadratic equation.
ax^{2} + bx + c = 0, a ≠ 0 is called the standard form of a quadratic equation.
For example, 2x^{2} + x – 30 = 0, 4x^{2} -2x + 5 = 0, 3x – 4x^{2} + 2 = 0 are all quadratic equations.
A real number α is called a root of the quadratic equation ax^{2} + bx + c = 0, a ≠ 0 if aα^{2} + bα + c = 0. We also say that x = α is a solution of the quadratic equation, or that α satisfies the quadratic equation. Note that the zeroes of the quadratic polynomial ax^{2} + bx + c and the roots of the quadratic equation ax^{2} + bx + c = 0 are the same.
A quadratic equation can only have two roots/zeroes.
We obtain the roots of a quadratic equation, ax^{2} + bx + c = 0 using this method by factoring the LHS into two linear parts and equating each element to zero. For example,
2x^{2} – 5x + 3 = 0
We split the middle term,
2x^{2} – 2x – 3x + 3 = 0 …..(i)
2x (x – 1) –3(x – 1) = 0
(2x – 3)(x – 1) = 0
2x – 3 = 0 or x – 1 = 0
x = 3/2 or x = 1
Necessary Condition - The product of the first and last terms of eq. (i) should be equal to the product of the second and third terms of the same equation.
This method involves adding and removing the appropriate constant terms to transform the L.H.S. of a quadratic equation that is not a perfect square into the sum or difference of a perfect square and a constant.
The roots of a quadratic equation ax^{2} + bx + c = 0 are given by:
provided b^{2} – 4ac ≥ 0
The value of (b^{2} – 4ac) is known as the discriminant of the equation and is denoted as D.
Q1. Why Should I Practice NCERT Solutions Class 10 Maths Chapter 4?
Answer: Quadratic equation is a topic that is not only essential in mathematics but also plays a vital part in many real-life events. The quadratic equation can be used to calculate the length and width of a garden. You can plan the quantity of grass carpet needed for the garden based on this information. Quadratic equations are frequently employed in astronomy, science, and architecture. Because of its wide range of applications, students should thoroughly practise the NCERT Solutions Class 10 Maths Chapter 4.
Q2. How many exercises are there in Chapter 4 of Class 10 Maths?
Answer: There are four exercises in the fourth chapter of NCERT Solutions for Class 10 Maths. Class 10 Maths Chapter 4 Quadratic Equations contains a total of 24 questions, 15 of which are simple, 5 of which are intermediate, and 4 of which are challenging. These questions are answered step by step. Students can answer all quadratic equation-based questions by completing these activities. In addition, the problems are answered in more than one way to help students learn basic quadratic equation ideas.
Q3. What major topics are addressed in NCERT Solutions Class 10 Maths Chapter 4?
Answer: Quadratic Equations are the foundation of Chapter 4 of Class 10 Maths. The important topics covered in NCERT Solutions Class 10 Maths Chapter 4 are how to mathematically represent the given problem statements, what is the standard form of a quadratic equation, and how to solve quadratic equations by factoring and completing the squares, which is an essential topic that requires regular practice.
Q4. In Class 10, how do you solve Quadratic Equations?
Answer: If you want to learn how to solve quadratic equations in Class 10, you can use the Toppr website or app to access NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations. All solutions are written in simple language by specialists. The equations are easily understood by students. Students must use the quadratic formula to discover the roots. They can compute the sum and product of both roots. The procedure is straightforward and well-explained for clarity.