Ex 4.2, 3 - Chapter 4 Class 10 Quadratic Equations

Transcript

Ex 4.2, 3 Find two numbers whose sum is 27 and product is 182. Let First number be x Given that Sum of both numbers is 27 First number + Second number = 27 x + Second number = 27 Second number = 27 – x Also given that, Product of both numbers = 182 First number × second number = 182 x (27 – x) = 182 27x – x2 = 82 0 = x2 – 27x + 182 x2 – 27 x + 182 = 0 We factorize by splitting the middle term method x2 – 13x – 14x + 182 = 0 x (x – 13) – 14 (x – 13) = 0 (x – 14) (x – 13) = 0 Hence, 13 & 14 are the roots of the equation Now, finding the numbers Hence, two numbers are 13 & 14 For x = 13 First number = x = 13 Second number = 27 – x = 27 – 13 = 14 For x = 14 First number = x = 14 Second number = 27 – x = 27 – 14 = 13 Thus, the two numbers are 13 and 14