The product of two consecutive positive integers is 306. Form the quadratic equation to find the integers, if x denoted the smaller integer.
Answers
Given : The product of two consecutive positive integers is 306.
solution :
Let two consecutive positive integers are x and (x + 1)
A.T.Q
Product of x and (x + 1) = 306
x(x + 1) = 306
x² + x = 306
x² + x - 306 = 0
Hence, x² + x - 306 = 0 is the required quadratic equation.
By factorisation,
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
But x ≠ -18 because x is a positive integer.
Therefore, x = 17
One positive integer (x) = 17
Other positive integer = x + 1 = 17 + 1 = 18
Hence, the two consecutive positive integers are 17 and 18 .
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Step-by-step explanation:
Hi ,
Let x and ( x + 1 ) are two consecutive positive
integers ,
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+ 18 = 0 or x -17 = 0
x = -18 or x = 17
But x is a positive integer,