Question

the product of two consecutive positive integers is 306write the quadratic equation to find the integer​

Answer 1

Answer:

The integers are 17 and 18.

Step-by-step explanation:

Let the consecutive integers be x, x+1

Now, according to the question, Their product is 306.

Hence, $x(x+1)=306$

Expanding, $x^2+x=306$

And, $x^2+x-306=0$

Hence, we have goth the quadratic equation.

Factorizing to find the roots, $x^2+18x-17x-306=0$

taking x and 17 common, $x(x+18)-17(x+18)\\(x+18)(x-17)=0$

Hence, we get the value of x to be either 17 or -18. But, as we are looking for positive integers, we do not consider -18. Hence, x= 17, x+1= 18.