Class 10 Maths

Quadratic Equation

NCERT Exercise 4.2

Part 2

Question 2: Solve the problems given in Example 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. We would like to find out how many marbles they had to start with.

Answer: Given, John and Jivanti together have number of marbles = 45

After losing of 5 marbles by each of them, number of marble `= 45 – 5 – 5 = 45 – 10 = 35`

Let us assume, John has x marbles

Hence; marbles with Jivanti `= 35 – x`

As per question; product of marbles after loss = 124

Therefore; `x(35 – x) = 124`

Or, `35x – x^2 = 124`

Or, `- x^2 + 35x – 124 = 0`

Or, `x^2 – 35x + 124 = 0`

Or, `x^2 – 4x – 31x + 124 = 0`

Or, `x(x – 4) – 31 (x – 4) = 0`

Or, `(x – 31)(x – 4) = 0`

Hence, `x = 31` and `x = 4`

One person has 31 marbles and another has 4 marbles

At the beginning; one person had 36 marbles and another had 9 marbles.

(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 Rs 750. We would like to find out the number of toys produced on that day.

Answer: Let us assume, number of toys `= x`

Then, cost of production of each toy `= x – 55`

Hence, total cost of production `= x(55 – x) = 750`

Or, `55x – x^2 = 750`

Or, `x^2 - 55x + 750 = 0`

Or, `x^2 - 30x - 25x + 750 = 0`

Or, `x(x - 30) – 25(x – 30) = 0`

Or, `(x – 25)(x – 30) = 0`

Hence, `x = 25` and `x = 30`

Thus, number of toys is 25 or 30

Question 3: Find two numbers whose sum is 27 and product is 182.

Answer: Let us assume, one of the numbers `= x`

Hence, second number `= 27 – x`

As per question; `x(27 – x) = 182`

Or, `27x – x^2 = 182`

Or, `27x – x^2 – 182 = 0`

Or, `x^2 – 27x + 182 = 0`

Or, `x^2 – 14x – 13x + 182 = 0`

Or, `x(x – 14) – 13(x – 14) = 0`

Or, `(x – 13)(x – 14) = 0`

Hence, `x = 13` and `x = 14`

Hence, the numbers are 13 and 14


Real Number

Real numbers include both rational and irrational numbers.

Polynomials

Polynomials are mathematical expressions containing variables and coefficients.

Linear Equations

Linear Equation is an equation with highest power of variable as 1

Quadratic Equations

A polynomial of 2nd degree is called quadratic equation

Arithmetic Progression

Arithmetic Progression is a sequence of numbers in which difference between any two consecutive numbers is constant.

Triangles

Triangle is a three sided polygon in which all sides are straight lines.

Coordinate Geometry

Coordinate Geometry is study of geometric figures by plotting them on coordinate axes.

Trigonometry

Trigonometry deals with relationship between angles and sides of a triangle.

Circle & Tangent

A line touching a circle at a single point is called tangent to the circle.

Practical Geometry

Geometry Construction is an integral part of practical geometry.

Area of Circle

Area of Circle is equal to the product of pi and square of radius of circle.

Surface Area & Volume

Read about surface area and volume of cube, cylinder, cone and sphere.

Statistics

Read about data analysis using mean, mode and median.

Probability

Probability tells about likelihood of an event to occur.