Chapter 4 · Quadratic Equations

NCERT Class 10 Maths Exercise 4.2

All 6 questions of NCERT Class 10 Maths Exercise 4.2 (Quadratic Equations), in the book's order, each with its answer and a step-by-step solution.

1. Q1
   Find the roots ​of ​the ​following quadratic equations ​by ​factorisation: ​

   1. (i)$x^2-3x-10=0$ ​
   2. (ii)$2x^2+x-6=0$ ​
   3. (iii)$\sqrt{2}{x}^2+7x+5\sqrt{2}=0$
   4. (iv)$2x^2-x+\frac{1}{8}=0$
   5. (v)$100x^2-20x+1=0$
   Show answer

   (i) $x=5,-2$; (ii) $x=\frac{3}{2},-2$; (iii) $x=-\frac{5\sqrt{2}}{2},-\sqrt{2}$; (iv) $x=\frac{1}{4}$ (equal roots); (v) $x=\frac{1}{10}$ (equal roots).

   Step-by-step solution →
2. Q2
   Solve the problems given in Example 1. ​[Example 1:

   1. (i)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 how many marbles they had to start with.
   2. (ii)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 ​the number of toys ​produced on that day.]
   Show answer

   (i) The marbles satisfy $x^2-45x+324=0$, so $x=36$ or $x=9$ — John and Jivanti started with 36 and 9 marbles. (ii) The toys satisfy $x^2-55x+750=0$, so $x=25$ or $x=30$ — either number of toys is possible.

   Step-by-step solution →
3. Q3
   Find ​two numbers ​whose sum ​is ​27 ​and product ​is 182.
   Show answer

   The two numbers are $13$ and $14$.

   Step-by-step solution →
4. Q4
   Find ​two consecutive positive ​integers, sum of ​whose ​squares ​is ​365.
   Show answer

   The two consecutive positive integers are $13$ and $14$.

   Step-by-step solution →
5. 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.
   Show answer

   Base $=12$ cm and altitude $=5$ cm.

   Step-by-step solution →
6. 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 Rs. $90$, find ​the number of articles produced and the cost of each article.
   Show answer

   Number of articles $=6$ and cost of each article $=$ Rs. $15$.

   Step-by-step solution →