The product of two consecutive positive integers is 1,332. Describe how to create and solve a quadratic equation to determine the greater integer's value.

Question

The product of two consecutive positive integers is 1,332. Describe how to create and solve a quadratic equation to determine the greater integer&#039;s value.

Gennenzip · Accepted Answer

Let x be the smaller of the consecutive positive integers. Consecutive integers are 1 away from each other so the larger integer must be x+1.&amp;nbsp;The product of the two consecutive positive integers is then x(x+1) so if the product is 1,332, then x(x+1)=1,332.&amp;nbsp;To solve this quadratic equation, first distribute the term with x to get&amp;nbsp;x2+x=1,332.&amp;nbsp;Subtracting 1,332 on both sides then gives&amp;nbsp;x2+x−1,332=0.&amp;nbsp;To factor&amp;nbsp;x2+x−1,332=0, find two numbers that when multiplied together equal −1,332 since the constant is −1,332 and add to 11 since the middle term has a coefficient of 11. Those two numbers are 37 and −36 since 37(−36)=−1,332 and 37+(−36)=1.&amp;nbsp;The factored form of the quadratic equation is then (x+37)(x−36)=0.&amp;nbsp;Set each element to 0 and then resolve each linear equation for x.Setting the first factor equal to 0 gives x+37=0. Subtracting 37 on both sides gives x=−37. The integers must be positive though so the smaller integer cannot be −37.&amp;nbsp;Setting the second factor equal to 0 gives x−36=0. Addin 36 on both sides gives x=36.&amp;nbsp;The smaller integer is then 36 and the larger integer is x+1=36+1=37.

Accepted Answer

The numbers can be written as x and x + 1. Set the product of the numbers equal to 1,332 to get x(x + 1) = 1,332. You can solve the quadratic equation by using the quadratic formula, completing the square, or factoring. When you solve the quadratic equation, you find that x = –37 and 36. Since the question asked for positive integers, the only viable solution is x = 36. To solve for the larger integer, you add 1 to 36 to get an answer of 37.

Vasquez · Accepted Answer

We can start by using n to represent the smaller of the two consecutive positive integers, and n+1 to represent the larger integer.We are given that their product is 1,332, so we can set up the equation:(n)(n+1)=1332Expanding the left side of the equation:n2+n=1332Bringing everything to one side:n2+n−1332=0This is a quadratic equation in standard form ax2+bx+c=0, where a=1, b=1, and c=−1332. We can solve for n using the quadratic formula:n=−b±b2−4ac2aSubstituting the values for a, b, and c:n=−1±12−4(1)(−1332)2(1)Simplifying the expression inside the square root:n=−1±53292We can disregard the negative solution since we are looking for a positive integer, so:n=−1+53292Simplifying the expression inside the square root:n=−1+732n=36Therefore, the greater integer is n+1=36+1=37.

RizerMix · Accepted Answer

We know that the product of two consecutive positive integers can be expressed as n(n+1). In this case, we have n(n+1)=1332.Let&#039;s try to factor 1332 into two factors that are consecutive integers. One way to do this is to use trial and error:1332=2·666=3·444=4·333=6·222=9·148=12·111=18·74=37·36We see that 37 and 36 are consecutive integers whose product is 1332. Therefore, the greater integer is 37.

Jeffrey Jordon · Accepted Answer

Answer:37Explanation:The problem can be solved by letting x be the smaller integer. Then, the next consecutive integer will be x+1. The product of these two integers is given as 1,332.We can write this as the quadratic equation:x(x+1)=1,332Expanding the left-hand side:x2+x=1,332Moving all the terms to one side:x2+x−1,332=0Now, we can solve this quadratic equation using the quadratic formula:x=−b±b2−4ac2awhere a=1, b=1, and c=−1,332.Plugging in these values:x=−1±12−4(1)(−1,332)2(1)Simplifying:x=−1±1+5,3282x=−1±5,3292Since we are looking for the greater integer, we can use the positive root:x=−1+5,3292x≈36.64Rounding up to the nearest integer, we get x=37, which is the greater integer. Therefore, the solution to the problem is 37.

The product of two consecutive positive integers is 1,332 Explain how you can write and solve a quadratic equation to find the value of the larger integer.

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