Question

the product of the two consecutive positive integers is 156 form a quadratic equation for the above situation ​

Answer 1

Let x and (x + 1) be the two consecutive positive integers.

We have to find, the two consecutive positive integers are:

Solurion:

According to question:

The product of the two consecutive positive integers = 156

∴ x(x + 1) = 156

⇒ $x^{2}$ + x = 156

⇒ $x^{2}$ + x - 156 = 10, this is the quadratic equation.

$x^{2}$ + 13x - 12x - 156 = 0

⇒ x(x + 13) - 12(x + 13) = 0

⇒ (x + 13)(x - 12) = 0

⇒ x + 13 = 0 or, x - 12 = 0

⇒ x = - 13  or, x = 12

⇒ x = 12  [ ∵ - 13 is not a positive integer]

∴ x + 1 = 12 + 1 = 13

Thus, the two consecutive positive integers are "12 and 13".

Answer 2

Given:

The product of the two consecutive positive integers is 156.

To find:

Form a quadratic equation.

Solution:

From given, we have the data as follows.

The product of the two consecutive positive integers is 156.

Let 'x' be the number and it's consecutive positive integer be "(x + 1)".

Then, from the given condition, we have,

x (x + 1) = 156

x² + x = 156

x² + x - 156 = 0

Therefore, the required quadratic equation is, x² + x - 156 = 0.

Now, let us find out the zeros of this equation.

So, we have,

x² + x - 156 = 0

(x - 12) (x + 13) = 0

x = 12, -13

Therefore, the zeros of x² + x - 156 = 0 are x = 12, -13.