Question 711687
{{{ graph( 300, 200, -15, 15, -10, 30, x^2+x+1,y=5,y=10,y=15,y=20) }}}
Yes, there are values of n that produce multiples of 5. On the graph lines are drawn when Y=5, Y=10, Y=15 & Y=20. However the values of n that produce a multiple of 5 may not be whole numbers.
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For example we can solve for what value of n makes the equation equal 10.
{{{n^2 + n + 1 = 10}}}
Subtract 10 from both sides
{{{n^2 + n - 9 = 0}}}
Now we can use the quadratic equation to solve for n
*[invoke quadratic "n", 1,1,-9]
The quadratic shows us that when n is equal to -3.54 or 2.54, the equation is equal to 10, which is a multiple of five.