Question

# The product of two consecutive positive integers is 240. Formulate the quadratic equation whose roots are these integers.

Hint: The product of two roots is given. So the value of the $1^{st}$ multiplied by the $2^{nd}$ root is 240. Then we need to equate the two and find the value of the root.

Complete step by step solution: Given, The product of two consecutive positive integers is 240.
We need to select two consecutive i.e. values which come after each other.
Therefore,
Let the two consecutive positive integers be x and(x+1),
Here we take x as the first integer and so the next number coming after it is (x+1)
For example, 2 comes after 1 and 2=1+1
Then according to the problem,
Their product is;
x(x+1)=240
On multiplying the two variables on the left hand side we get,
$x^{2}-x-240=0$
This is the required quadratic equation. Thus, when two consecutive positive integers are multiplied we get the equation we got above.

Note: The standard form of a quadratic equation is $a{x}^{2}+bx+c=0$, where a, b and c are real numbers and $a\ne 0$. 'a' is the coefficient of ${x}^{2}$. It is called the quadratic coefficient. 'b' is the coefficient of x. Students often go wrong in calculating the coefficients. Students also tend to make mistakes in solving the quadratic equations which is not needed here.