Welcome to the Chapter 4 - Quadratic Equations, Class 10 Mathematics - NCERT Solutions page. Here, we provide detailed question answers for Chapter 4 - Quadratic Equations.The page is designed to help students gain a thorough understanding of the concepts related to natural resources, their classification, and sustainable development.
Our solutions explain each answer in a simple and comprehensive way, making it easier for students to grasp key topics Solving quadratic equations by factorization and quadratic formula, discriminant and nature of roots and excel in their exams. By going through these Quadratic Equations question answers, you can strengthen your foundation and improve your performance in Class 10 Mathematics. Whether you're revising or preparing for tests, this chapter-wise guide will serve as an invaluable resource.
Download PDF - Chapter 4 Quadratic Equations - Class 10 Mathematics
Download PDF - NCERT Examplar Solutions - Chapter 4 Quadratic Equations - Class 10 Mathematics
Find the nature of the roots of the following quadratic equations. If the real roots exist, find them:
(i) 2x2 – 3x + 5 = 0 (iii) 2x2– 6x + 3 = 0
Is the following situation possible? If so, determine their present ages.
The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.
Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30°, respectively. Find the height of the poles and the distances of the point from the poles.
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 each 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 number of articles produced and the cost of each article.
Find two consecutive positive integers, sum of whose squares is 365.
Find two numbers whose sum is 27 and product is 182.
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is:
(i) intersecting lines (ii) parallel lines (iii) coincident lines
Refer to Example 13. (i) Complete the following table:
(ii) A student argues that ‘there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore, each of them has a probability
Do you agree with this argument? Justify your answer.
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.
(i) x2 – 2x – 8 (ii) 4s2 – 4s + 1 (iii) 6x2 – 3 – 7x (iv) 4u2 + 8u (v) t2 – 15 (vi) 3x2 – x – 4
Is the following situation possible? If so, determine their present ages.
The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30° (see Fig. 9.11).
From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower.
Sum of the areas of two squares is 468 m2. If the difference of their perimeters is 24 m, ind the sides of the two squares.
Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.
12 defective pens are accidentally mixed with 132 good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is taken out at random from this lot. Determine the probability that the pen taken out is a good one.
Prove that 3 + 2√5 is irrational.
In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.
Why is tossing a coin considered to be a fair way of deciding which team should get the ball at the beginning of a football game?