Question

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

Answer 1

Hey there !!!!!

Let numbers be x and x+1
so, x(x+1)=240
   x²+x-240=0 is required quadratic equation.

Answer 2

Required equation: x² - 31x + 240 = 0

Step-by-step explanation:

We proceed by factorizing 240.

• Refer to the attached image.

We have: 240 = 2 × 2 × 2 × 2 × 3 × 5

From this we find two positive integers by products of factors: (3 × 5) and (2 × 2 × 2 × 2), that is, 15 and 16. These are consecutive integers.

So, the required quadratic equation is

(x - 15) (x - 16) = 0

⇒ x² - 16x - 15x + 240 = 0

⇒ x² - 31x + 240 = 0

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