product of roots was 1 (constant term was 2, and coefficient on x^4 term was 2) lines question was 13 as there were 16 lines in total, so its clear that y = 1 - 10x is gonna 'touch' all 16, but take away 3 from 16 as 3 points are intersections between all three graphs (namely at y = 0, -1/3, -2/3 if i remember correctly)
I can't believe i misread product of roots.That's one of the worst things i've ever done on a test.
Same I also put 15 ,explain a bit on why you think it was 13 because i think thats probably true now that i started thinking about it more.I also got 9/10 for the sum things.
Each of the lines are of the form y = -x+c (c = numbers 1-7) and y = 2x+k (k numbers 1-9). There are 16 lines and the line -10x +1 crosses each of these once. What the question was essentially asking was where were the intersections of all 3 lines. We can work out that the x coordinates of the points of intersection can be expressed as 9x = c-1 and 12x = k-1. You're therefore looking for the points where (c-1)/9 = (k-1)/12. These are 0/9 = 0/12 (k=1 c=1), 3/9 = 4/12 (c=4 k=5) and 6/9 = 8/12 (k=9 c=7). Thus there are 3 points where all 3 lines intersect. Therefore there are 16 (total intersections) - 3 ("crossovers") =13. That was my reasoning at least.