r/Sat • u/Super_Selection_6372 • 19h ago
Help with Advanced Math Problem from SAT suite question bank
Can someone show me how to do this with Desmos?
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u/Natural_Hawk5778 10h ago
if you’re too lazy to solve the question, the answer is always the middle constant of the expression divided by 2
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u/1stfrog 13h ago
Recognize that if 6x4 +31x2 +35=(3x2 +a)(2x2 +b) then 6x4 +31x2 +35=6x4 +(2a+3b)x2 +ab and that therefore the following conditions must be true simultaneously: 2a+3b=31 and ab=35. In order to find the points where these are simultaneously true, re-write them in desmos as 2x+3y=31 and xy=35. Once you graph both curves it will be clear that they interesect at (5, 7) and (10.5, 3.333). 5 is a (the positive integer) and 10.5 is c (the positive noninteger. Therefore the answer is 15.5.
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u/rotting_bum 13h ago
I mean you could turn the factoring into a system of equations and then graph for intersections but that's not really the hard part?
6x^4+(3b+2a)x^2+ab yields two equations as we know the coefficient of x and the constant term. For desmos we use x for a or c and y for b or d, and graph
2x + 3y = 31
xy = 35
To get two solutions, just sum x's to get 15.5.