Algebra: Consecutive Integers Problem

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Questions and Answers

What is the equation used to find two consecutive positive integers whose product is 306?

  • $2x^2 + 2x = 306$
  • $x(x + 2) = 306$
  • $x^2 + 1 = 306$
  • $x(x + 1) = 306$ (correct)

What form does the quadratic equation take after simplifying $x(x + 1) = 306$?

  • $x^2 - 306 = 0$
  • $x^2 + 306 = 0$
  • $x^2 + 2x - 306 = 0$
  • $x^2 + x - 306 = 0$ (correct)

What is the significance of the number 26 mentioned in the problem?

  • It is the age of the mother. (correct)
  • It represents the sum of the integers.
  • It is the age of the child.
  • It is the product of two integers.

What do the equations in the problem primarily involve?

<p>Solving for unknown values using multiplication. (A)</p>
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Which of the following concepts is likely addressed by the problem involving consecutive integers?

<p>Quadratic equations (B)</p>
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Flashcards

Consecutive positive integers

Numbers that follow each other in order, with a difference of 1.

Solving equations

Finding the value of unknown variables in a mathematical equation.

Product of integers

The result obtained when multiples integers together.

Quadratic equation

A polynomial equation of degree 2, typically in the form ax² + bx + c = 0.

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Finding ages

Using equations and given information to find the ages of people.

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x(x + 1) = 306

An equation representing the product of two consecutive positive integers equaling 306.

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x² + x – 306 = 0

Simplified form of x(x + 1) = 306, arranged to solve for x.

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2x² + 2x – 528 = 0

Another equation, possibly representing additional or alternative calculations in the problem.

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