Question

find two numbers whose sum is 27 and product is 182​

Answer 1

Answer:

13 and 14

Step-by-step explanation:

Let the numbers be α and β.

A.T.Q.

α + β = 27

αβ = 182

Using the concept of quadratic polynomial, we get an equation :

→ p(x) = k [x² - (α + β)x + αβ]

Putting known values, we get

→ p(x) = k [x² - (27)x + 182]

→ p(x) = k [x² - 27x + 182]

Putting k = 1, we get

→ p(x) = x² - 27x + 182

Solving the above equation by Middle Term Factorisation

→ p(x) = x² - 13x - 14x + 182

→ p(x) = x(x - 13) - 14(x - 13)

→ p(x) = (x - 14)(x - 13)

Using Zero Product Rule

→ (x - 14) = 0 and (x - 13) = 0

→ x = 14 and x = 13

Hence, the two numbers are 13 and 14.

Answer 2

Answer:

Let one number be X

and Second one be Y

According to Condition 1

x ( 27 - x ) = 182

$27x - {x}^{2} = 182 \\ { x}^{2} - 27x + 182 = 0 \\ \\ \\ \\ {x}^{2} - 14x - 13x + 182 = 0 \\ x(x - 14x) - 13(x - 14) = 0 \\ (x - 14)(x - 13) \\ \\ \\ x = 13 \: and \: 14 \\ \\ \\ \\ first \: no \: 13 \\ second \: no \: 14 \:$

or first no 14

second no 13