the product of two consecutive integers is 342. which quadratic equation can be used to find x, the greater…

the product of two consecutive integers is 342. which quadratic equation can be used to find x, the greater number?\n$x^{2}+1 = 342$\n$x^{2}-1 = 342$\n$x^{2}-x + 342 = 0$\n$x^{2}-x - 342 = 0$

the product of two consecutive integers is 342. which quadratic equation can be used to find x, the greater number?\n$x^{2}+1 = 342$\n$x^{2}-1 = 342$\n$x^{2}-x + 342 = 0$\n$x^{2}-x - 342 = 0$

Answer

Explanation:

Step1: Let the two consecutive integers

Let the smaller integer be (x - 1) and the greater integer be (x).

Step2: Set up the product - equation

The product of the two consecutive integers is ((x-1)\times x=342).

Step3: Expand the left - hand side

Expand ((x - 1)x) using the distributive property (a(b - c)=ab-ac). Here (a = x), (b=x), (c = 1), so ((x - 1)x=x^{2}-x). Then the equation becomes (x^{2}-x=342).

Step4: Rearrange to quadratic form

Subtract 342 from both sides of the equation (x^{2}-x = 342) to get (x^{2}-x - 342=0).

Answer:

(x^{2}-x - 342 = 0)