The product of two consecutive integers is 342. Which quadratic equation can be used to find x, the greater number?

Question

pythagoras123 · Answer

Since the greater number has value x, the smaller number must be (x-1). 
(x)(x-1)=342  (product of two consecutive integers) 
x^2 - x = 342  (expand brackets)

pythagoras123 · Answer

$$x^2 - x = 342$$

silverfang492 · Answer

Set greater number as x. x(x-1)=342, according to your problem. When you multiply it out, you have $$x^2-x=342.$$ Then, you move 342 to the other side and you have $$x^2-x-342=0.$$
Finally, you factor and you are left with (x-19)(x+18) or (x+19)(x-18). This means that x can be $$\pm19$$ and $$\pm18$$

silverfang492 · Answer

which means that the bigger one is 19 or -19, and the smaller is 18, or -18 (positive if 19 is positive, negative if 19 is negative)

robtobey2 · Answer

Refer to the Mathematica attachment.