Solve the equation x 2 - 12 x + 27 = 0 by using formula.

Given equation is x 2 - 12 x + 27 = 0 Comparing with a x 2 + b x + c = 0 , we get a = 1 , b = - 12 , c = 27 D = b 2 - 4 a c = - 12 2 - 4 1 27 = 144 - 108 = 36 We know that x = - b ± b 2 - 4 a c 2 a ⇒ x = - - 12 ± 36 2 × 1 ⇒ x = 12 ± 6 2 ∴ x = 18 2 = 9 a n d x = 6 2 = 3

A dealer sells an article for ₹ 16 and loses as much per cent as the cost price of the article. Find the cost price of the article.

Given, dealer sells an article for ₹ 16 and loses as much per cent as the cost price of the article. Let the cost price of the article be ₹ x . Loss = x % of ₹ x = ₹ x 100 × x = ₹ x 2 100 Cost price - Loss = Selling price ∴ x - x 2 100 = 16 ⇒ 100 x - x 2 - 1600 100 = 0 ⇒ x 2 - 100 x + 1600 = 0 ⇒ x 2 - 80 x - 20 x + 1600 = 0 ⇒ x x - 80 - 20 x - 80 = 0 ⇒ x - 80 x - 20 = 0 ⇒ x - 80 = 0 or x - 20 = 0 ⇒ x = 80 or x = 20 Hence, the cost price of the article is ₹ 80 or ₹ 20 .