# Ex.4.2 Q3 Quadratic Equations Solutions - NCERT Maths Class 10

## Question

Find two numbers whose sum is \(27\) and product is \(182.\)

## Text Solution

**What is known?**

(i) Sum of two numbers is \(27.\)

(ii) Product of two numbers is \(182.\)

**What is Unknown?**

Two numbers.

**Reasoning:**

Let one of the numbers be \(x\). Then the other number will be

\(x +\) other number \(= 27\)

Other number \(= 27 – x\)

Product of the two numbers \(= 182\)

This can be written in the form of the following equation:

\[x\left( {27 - x} \right) = 182\]

**Steps:**

\[\begin{align}x\left( {27 - x} \right) &= 182\\27x - x &= 182\\27x - x - 182 &= 0\\x - 27x + 182 &= 0\\x - 14x-13x + 182 &= 0\\x\left( {x - 14} \right)-13\left( {x - 14} \right) &= 0\\\left( {x - 13} \right)\left( {x - 14} \right) &= 0\\x-13 = 0 & \qquad x-14 = 0\\x = 13 & \qquad x = 14\end{align}\]

The numbers are \(13,\, 14.\)