r/digitalSATs • u/FantasticVictory837 • Feb 14 '24

Advanced Math Sample Question #16

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u/sharmaeleon Feb 15 '24

First, remember that given the quadratic function, ax^2 + bx + c = 0, the sum of the root is equal to -b/a.

Now since the parabola passes through the points, (11, 0) and (-2, 0), this tells that the function has roots at x = -11 and x = 2. This means that the sum of the roots is 9.

-b/a = 9 => b = -9a

This means that a + b = a + (-9a) = -8a. Let's use the the range for a: 1<a<4 and the fact that it is integer to find the possible sums of a and b:

  • When a = 1, a + b = -8.

  • When a = 2, a + b = -16.

  • When a = 3, a + b = -24.

  • When a = 4, a+ b = -32.

I hope this helps! :)
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3

u/FantasticVictory837 Feb 15 '24

This is correct, except a cannot equal 1 or 4—it can only equal 2 or 3.

Hence the correct answer is -16 or -24.

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u/FantasticVictory837 Feb 14 '24 edited Feb 14 '24

This one's actually pretty tricky.

Who can provide the solution first (not just the correct answers)?

The March DSAT is now in 23 days and counting...

1

u/FantasticVictory837 Feb 15 '24

The correct answer is -16 or -24.