Question

Represent the following situations in the form of quadratic equation: (a) The product of two consecutive positive integers is 342. We need to find the integers?​

Answer 1

let two consecutive integers be x and( x +1)

x ( x + 1)= 342

x2 + x = 342

x2 + x -342 = 0 is a quadratic equation.

Answer 2

The integer is x.

1 added to the integer is x+1.

The equation is x(x+1)=342,

but also requires x>0.

After we find the equation:

x²+x=342

x²+x-342=0

x²+19x-18x+342=0

x(x+19)-18(x+19)=0

(x-18)(x+19)=0

The positive root is x=18.

Therefore the required positive integer pair is 18 and 19.