The Product Of Two Consecutive Positive Integers Is 306. Find The Integers. CBSE 2020 (Basi​

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The Product of Two Consecutive Positive Integers is 306: A CBSE 2020 Problem

The Central Board of Secondary Education (CBSE) is one of the most prestigious educational boards in India, and its exams are a benchmark for students' knowledge and skills. In the CBSE 2020 exams, students were presented with a variety of problems that tested their mathematical skills. One such problem was to find the product of two consecutive positive integers that equals 306. In this article, we will discuss the solution to this problem and provide a step-by-step guide to help students understand the concept.

The problem states that the product of two consecutive positive integers is 306. This means that if we have two consecutive integers, say x and x+1, their product should be equal to 306. Mathematically, this can be represented as:

x(x+1) = 306

To solve this problem, we need to break it down into smaller steps. Let's start by expanding the equation:

x(x+1) = 306

Expanding the left-hand side of the equation, we get:

x^2 + x - 306 = 0

This is a quadratic equation in the form ax^2 + bx + c = 0, where a = 1, b = 1, and c = -306.

To solve the quadratic equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = 1, b = 1, and c = -306. Plugging these values into the formula, we get:

x = (-(1) ± √((1)^2 - 4(1)(-306))) / 2(1) x = (-1 ± √(1 + 1224)) / 2 x = (-1 ± √1225) / 2 x = (-1 ± 35) / 2

Now that we have the solutions to the quadratic equation, we need to find the values of x that satisfy the equation. We have two possible solutions:

x = (-1 + 35) / 2 x = 34 / 2 x = 17

x = (-1 - 35) / 2 x = -36 / 2 x = -18

Now that we have the solutions, we need to check if they satisfy the original equation. Let's plug in x = 17 and x = 18 into the original equation:

x(x+1) = 306

For x = 17:

17(17+1) = 17(18) = 306

For x = 18:

18(18+1) = 18(19) ≠ 306

In this article, we discussed the problem of finding the product of two consecutive positive integers that equals 306. We broke down the problem into smaller steps, solved the quadratic equation, and found the solutions. We then checked the solutions to ensure that they satisfy the original equation. The final answer is x = 17 and x+1 = 18.

  • The product of two consecutive positive integers is 306.
  • The quadratic equation x^2 + x - 306 = 0 can be solved using the quadratic formula.
  • The solutions to the quadratic equation are x = 17 and x = -18.
  • The solution x = 17 satisfies the original equation.
  • Find the product of two consecutive positive integers that equals 420.
  • Solve the quadratic equation x^2 + 2x - 35 = 0.
  • Find the solutions to the quadratic equation x^2 - 4x - 5 = 0.
  • CBSE 2020 Exams
  • Quadratic Formula
  • Algebraic Equations
    The Product of Two Consecutive Positive Integers is 306: A CBSE 2020 Problem - Q&A

In our previous article, we discussed the problem of finding the product of two consecutive positive integers that equals 306. We broke down the problem into smaller steps, solved the quadratic equation, and found the solutions. In this article, we will provide a Q&A section to help students understand the concept better.

Q: What is the product of two consecutive positive integers? A: The product of two consecutive positive integers is the result of multiplying two consecutive integers together. For example, if we have two consecutive integers 5 and 6, their product is 5 × 6 = 30.

Q: How do we find the product of two consecutive positive integers that equals 306? A: To find the product of two consecutive positive integers that equals 306, we need to solve the quadratic equation x^2 + x - 306 = 0. We can use the quadratic formula to solve this equation.

Q: What is the quadratic formula? A: The quadratic formula is a mathematical formula that is used to solve quadratic equations. It is given by:

x = (-b ± √(b^2 - 4ac)) / 2a

Q: How do we use the quadratic formula to solve the equation x^2 + x - 306 = 0? A: To use the quadratic formula, we need to plug in the values of a, b, and c into the formula. In this case, a = 1, b = 1, and c = -306. Plugging these values into the formula, we get:

x = (-(1) ± √((1)^2 - 4(1)(-306))) / 2(1) x = (-1 ± √(1 + 1224)) / 2 x = (-1 ± √1225) / 2 x = (-1 ± 35) / 2

Q: What are the solutions to the quadratic equation x^2 + x - 306 = 0? A: The solutions to the quadratic equation x^2 + x - 306 = 0 are x = 17 and x = -18.

Q: Which solution satisfies the original equation? A: The solution x = 17 satisfies the original equation.

Q: What is the product of the two consecutive positive integers that equals 306? A: The product of the two consecutive positive integers that equals 306 is 17 × 18 = 306.

Q: Can we find the product of two consecutive positive integers that equals 420? A: Yes, we can find the product of two consecutive positive integers that equals 420. We can use the same method as before to solve the quadratic equation x^2 + x - 420 = 0.

Q: How do we solve the quadratic equation x^2 + 2x - 35 = 0? A: To solve the quadratic equation x^2 + 2x - 35 = 0, we can use the quadratic formula. Plugging in the values of a, b, and c into the formula, we get:

x = (-(2) ± √((2)^2 - 4(1)(-35))) / 2(1) x = (-2 ± √(4 + 140)) / 2 x = (-2 ± √144) / 2 x = (-2 ± 12) / 2

Q: What are the solutions to the quadratic equation x^2 + 2x - 35 = 0? A: The solutions to the quadratic equation x^2 + 2x - 35 = 0 are x = 5 and x = -7.

Q: How do we solve the quadratic equation x^2 - 4x - 5 = 0? A: To solve the quadratic equation x^2 - 4x - 5 = 0, we can use the quadratic formula. Plugging in the values of a, b, and c into the formula, we get:

x = (4 ± √((-4)^2 - 4(1)(-5))) / 2(1) x = (4 ± √(16 + 20)) / 2 x = (4 ± √36) / 2 x = (4 ± 6) / 2

Q: What are the solutions to the quadratic equation x^2 - 4x - 5 = 0? A: The solutions to the quadratic equation x^2 - 4x - 5 = 0 are x = 9 and x = -1.

In this article, we provided a Q&A section to help students understand the concept of finding the product of two consecutive positive integers that equals 306. We discussed the quadratic formula and how to use it to solve quadratic equations. We also provided solutions to other quadratic equations to help students practice their skills.

  • The product of two consecutive positive integers is the result of multiplying two consecutive integers together.
  • To find the product of two consecutive positive integers that equals 306, we need to solve the quadratic equation x^2 + x - 306 = 0.
  • The quadratic formula is a mathematical formula that is used to solve quadratic equations.
  • The solutions to the quadratic equation x^2 + x - 306 = 0 are x = 17 and x = -18.
  • The solution x = 17 satisfies the original equation.
  • Find the product of two consecutive positive integers that equals 420.
  • Solve the quadratic equation x^2 + 2x - 35 = 0.
  • Find the solutions to the quadratic equation x^2 - 4x - 5 = 0.
  • CBSE 2020 Exams
  • Quadratic Formula
  • Algebraic Equations