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NCERT Solutions Class 10 Maths Chapter 4 Quadratic Equations - Free PDF

When we equate the quadratic polynomial to zero, then we get a quadratic equation. Latest : Trouble with homework? Post your queries of Maths and Science with step-by-step solutions instantly. Ask Mr AL. Q1 i Check whether the following are quadratic equations :. We have L. Therefore, can be written as:. This equation is of type:. Hence, the given equation is ncert solutions of chapter 4 class 10th maths quadratic equation. Q1 ii Check whether the following matus quadratic equations :.

Given equation can be written as:. Q1 iii Check whether the ncert solutions of chapter 4 class 10th maths are quadratic equations :. S can be written as:. The equation is of the type:. Q1 clasx Check whether the following are quadratic equations :. Q1 v Check whether the following are mahhs equations :.

Q1 vi Check whether the following are quadratic equations :. This equation is NOT of type:. Q1 vii Check whether the following are quadratic equations :. Hence, the given equation is not a quadratic chapteg.

Q1 viii Check whether the following are quadratic equations :. Q2 i Represent the following situations in the if of quadratic equations : The area of a rectangular plot is. The length of the plot in meters is naths more than twice its breadth. We need to find the length and breadth of the plot. Ncert solutions of chapter 4 class 10th maths the area of a rectangular plot is.

Let the breadth of the plot be. Then, jaths length of the plot will be:. Therefore the area will be:. Hence, the length and breadth of the plot will satisfy the equation. Q2 ii Represent the following situations in the form of quadratic equations : The product of two consecutive positive integers is We need to find the integers.

Given the product of two consecutive integers is. Let two consecutive integers be. Then, their product will be:. Hence, the two consecutive integers will satisfy this quadratic equation.

The product of their ages in years 3 years from now will be Let the age of Rohan be years. Then his mother age will be: years. After three years.

Rohan's age will be years and his mother age will be years. Then according to question. The product of their ages 3 years from now will be:. Hence, the age of Rohan satisfies the quadratic equation. Q2 iv Represent the following situations in the form of quadratic equations : A train travels a distance of km at a uniform speed.

We need to find the speed of the train. The 10yh to be covered by the train is. The time taken will be. If the speed had been less, the time taken would be:.

Now, according to question. Dividing by 3 on both the. Hence, the speed of the train satisfies coass quadratic equation. Q1 i Find the roots of the following ncrt equations by factorization:. Given the quadratic equation:. Factorization gives. Hence, the roots of the given quadratic equation are. Q1 ii Find the roots of the following quadratic equations by factorization:.

Factorisation gives. Q1 iii Find the roots of the following quadratic equations by factorization:. Q1 iv Find the roots of the following quadratic equations by factorization:. Solving the quadratic equations, we. Q1 v Find the roots of the following quadratic equations by factorization:. Q2 Solve the problems given in Example 1. From Example 1 we get:.

Solving by factorization method:. Therefore, John and Jivanti have 36 and 9 marbles respectively in the beginning. Therefore, the number of toys on that day.

Q3 Find two numbers whose sum is 27 and the product is Let two numbers be x and ncet. Then, their sum will be equal cass 27 and the product equals From equation 2 we have:.

Then putting the value of y in equation 1we. Solving this equation:. Hence, the two required numbers are. Q4 Find two consecutive positive integers, the sum of whose squares is Let the two consecutive integers be.

Then the sum of the squares is Hence, the ncert solutions of chapter 4 class 10th maths consecutive integers are. Q5 The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides. Let the length of the base of the triangle be. Then, the altitude length will sllutions. Given if hypotenuse is. Applying the Pythagoras theorem; we. But, the length of the base cannot be negative.

Hence the base length will be. Therefore, we clqss. Altitude length and Base length. Q6 A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of cahpter article in rupees was 3 more than twice the number of articles produced on that day.

If the total cost of production on that day was Rs 90, find the hcapter of articles produced and the cost ncert solutions of chapter 4 class 10th maths each article. Let the number of articles produced in ncert solutions of chapter 4 class 10th maths day. The cost of production of each article will be.

Given the total production on that day. Hence we soluhions the equation. But, x cannot be negative as it is the number of articles. Therefore, and the cost of each article. Hence, the number of articles is 6 and the cost of each article is Rs. Q1 i Find the roots of the following quadratic equations, if they exist, by the method of completing the square.

Solutoons equation:.

Main points:

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When a quadratic polynomial is equated to zero, it is called a quadratic equation. A zero of a polynomial is that real number, which when substituted for the variable makes the value of the polynomial zero. In case of a quadratic equation, the value of the variable for which LHS and RHS of the equation become equal is called a root or solution of the quadratic equation. There are three algebraic methods for finding the solution of a quadratic equation.

Brahmagupta an ancient Indian Mathematician A. Later Sridharacharya A. An Arab mathematician Al-khwarizni about A. It is believed that Babylonians were the first to solve quadratic equations. Greek mathematician Euclid developed a geometrical approach for finding lengths, which are nothing but solutions of quadratic equations.

The formulas are not easy to learn, and students don't catch tricks easily where they should apply. Chapter 4 Maths Class 10 contains quadratic equations to find the value of x. Apart from this, there are approximately three methods given in Class 10 Maths Chapter 4 for this. But, not all three methods are easy to understand to an individual. All concepts of quadratic equations and formulas have been explained well.

From where the formula comes, how it is discovered, by whom it is discovered, and many other things are mentioned first for the basic knowledge.

For the ease of the students, it is also mentioned which question came in which year. Some of the mock test papers are also available at the end of pdf for the students' better preparation.

Ncert Solutions Of Chapter 4 Class 10th Maths