Question

the product of two consecutive even integer is 528 represent it as a quadratic equation

Answer 1

x(x+2)=528
x²+2x=528
x² +2x-528=0

Answer 2

The statement, "the product of two consecutive even integers is 528", represented as a quadratic equation, will be x² + 2x - 528 = 0.

Given,

The product of two consecutive even integers is 528.

To find,

Represent the given statement as a quadratic equation.

Solution,

An even integer can be defined as the integer which is divisible by 2. A few examples of even integers are 2, 4, 6, 8, etc.

It can be seen that any two consecutive even integers will have a difference of 2 when the first is subtracted from the second. E.g. 4 - 2 = 2.

Now, to find the quadratic equation, first, let the two consecutive even integers be x and (x + 2).

The product of x and (x + 2) will be

x(x + 2)     ...(1)

It is given that their product is 528. Thus expression in (1) should equal 528.

⇒ x(x + 2) = 528

⇒ x² + 2x = 528

⇒ x² + 2x - 528 = 0, which is the required quadratic equation.

Therefore, the statement, "the product of two consecutive even integers is 528", represented as a quadratic equation, will be x² + 2x - 528 = 0.