Question

Find two numbers whose sum is 27 and product is 182.

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Answer 1

Step-by-step explanation:

Solution:

let the first number be x

Given that sum of both number is 27

so, first number+second number =27

x+ second number =27

second number = 27-x

also given that product of both number = 182

first number × second number = 182

x(27-x) = 182

27x-x2=82

0=x2- 27x+182

x2 - 27x+182 = 0

we factorize by

splitting the middle term method splitting the middle term method

x2-13x-14x+182=0 we need to find two numbers whose

x(x-13) - 14 (x-13) =0 sum = -27

(x-14) (x-13) = 0 product = 182×1=182

Sum Product

13 and 14 27 182

-13 and -14 -27 182

x-14=0 x-13=0

x=14 x=13

Hence 13 and 14 are the roots of the equation

For x= 13 For x=14

First number = x = 13 First number = x = 14

Second number = 27-x Second number = 27-x

=27-13=14 =27 - 14 =13

Hence, two numbers are 13 and 14