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NCERT Solutions · Maths Ch 4
Quadratic Equations
31 questions · 3 exercises
Closed
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Ex 4.1
Ex 4.2
Ex 4.3
NCERT answers with full exam-style working, step by step. Tap a question to open its solution.
1
12 QUESTIONS
Exercise 4.1
Q1(i)
Check whether the following is a quadratic equation: (x + 1)² = 2(x – 3)
(1 mark)
Q1(ii)
Check whether the following is a quadratic equation: x² – 2x = (–2)(3 – x)
(1 mark)
Q1(iii)
Check whether the following is a quadratic equation: (x – 2)(x + 1) = (x – 1)(x + 3)
(1 mark)
Q1(iv)
Check whether the following is a quadratic equation: (x – 3)(2x + 1) = x(x + 5)
(1 mark)
Q1(v)
Check whether the following is a quadratic equation: (2x – 1)(x – 3) = (x + 5)(x – 1)
(1 mark)
Q1(vi)
Check whether the following is a quadratic equation: x² + 3x + 1 = (x – 2)²
(1 mark)
Q1(vii)
Check whether the following is a quadratic equation: (x + 2)³ = 2x(x² – 1)
(1 mark)
Q1(viii)
Check whether the following is a quadratic equation: x³ – 4x² – x + 1 = (x – 2)³
(1 mark)
Q2(i)
Represent the following situation in the form of a quadratic equation: The area of a rectangular plot is 528 m². The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.
(2 marks)
Q2(ii)
Represent the following situation in the form of a quadratic equation: The product of two consecutive positive integers is 306. We need to find the integers.
(2 marks)
Q2(iii)
Represent the following situation in the form of a quadratic equation: Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.
(2 marks)
Q2(iv)
Represent the following situation in the form of a quadratic equation: A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.
(2 marks)
2
11 QUESTIONS
Exercise 4.2
Q1(i)
Find the roots of the following quadratic equation by factorisation: x² – 3x – 10 = 0
(2 marks)
Q1(ii)
Find the roots of the following quadratic equation by factorisation: 2x² + x – 6 = 0
(2 marks)
Q1(iii)
Find the roots of the following quadratic equation by factorisation: √2x² + 7x + 5√2 = 0
(2 marks)
Q1(iv)
Find the roots of the following quadratic equation by factorisation: 2x² – x + 1/8 = 0
(2 marks)
Q1(v)
Find the roots of the following quadratic equation by factorisation: 100x² – 20x + 1 = 0
(2 marks)
Q2(i)
Solve the problem: John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. Find out how many marbles they had to start with.
(3 marks)
Q2(ii)
Solve the problem: A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was ₹750. Find out the number of toys produced on that day.
(3 marks)
Q3
Find two numbers whose sum is 27 and product is 182.
(2 marks)
Q4
Find two consecutive positive integers, sum of whose squares is 365.
(2 marks)
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.
(3 marks)
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 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 ₹90, find the number of articles produced and the cost of each article.
(3 marks)
3
8 QUESTIONS
Exercise 4.3
Q1(i)
Find the nature of the roots of the following quadratic equation. If the real roots exist, find them: 2x² – 3x + 5 = 0
(2 marks)
Q1(ii)
Find the nature of the roots of the following quadratic equation. If the real roots exist, find them: 3x² – 4√3x + 4 = 0
(2 marks)
Q1(iii)
Find the nature of the roots of the following quadratic equation. If the real roots exist, find them: 2x² – 6x + 3 = 0
(3 marks)
Q2(i)
Find the value of k for the following quadratic equation, so that it has two equal roots: 2x² + kx + 3 = 0
(2 marks)
Q2(ii)
Find the value of k for the following quadratic equation, so that it has two equal roots: kx(x – 2) + 6 = 0
(2 marks)
Q3
Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m²? If so, find its length and breadth.
(3 marks)
Q4
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.
(3 marks)
Q5
Is it possible to design a rectangular park of perimeter 80 m and area 400 m²? If so, find its length and breadth.
(3 marks)