Question

If the product of two consecutive integers is 306, then write the quadratic representation of this situation.

Answer 1

Let two consecutive numbers are x and (x + 1) 
A/C to question,product of x and (x + 1) = 306 ⇒x(x + 1) = 306 ⇒x² + x - 306 = 0⇒ x² + 18x - 17x - 306 = 0⇒x(x + 18) - 17(x + 18) = 0⇒(x + 18)(x - 17) = 0⇒ x = 17 and -18
Hence, numbers are x = 17 and (x +1) = 18