SAT Math formula sheet · all 24 · Advanced Math · #10 of 24

The discriminant on the SAT: How It Is Tested

Nonlinear equations in one variable and systems of equations in two variables

Discriminant diagram for the SAT: Two things to spot: you need a quadratic, and a sentence telling you how many solutions. That is a discriminant problem.
What it is really testingTwo things to spot: you need a quadratic, and a sentence telling you how many solutions. That is a discriminant problem. Know the 3 cases: greater than 0 for 2 solutions, equal to 0 for 1 solution, and less than 0 for no solution. Then let Desmos solve it.

The question from the sheet

Hard
SAT Advanced Mathanswer B
In the given equation, cc is a constant. The equation has exactly one solution. What is the value of cc?
−3x2+24x+c=0-3x^{2} + 24x + c = 0
A-96
✓-48
C-32
D0

How the diagram applies

  1. Read off a=−3a = -3, b=24b = 24, c=cc = c. Everything is already on one side.
  2. Exactly one solution is case ii: b2−4ac=0b^{2} - 4ac = 0.
  3. 576−4(−3)(c)=576+12c=0576 - 4(-3)(c) = 576 + 12c = 0, so c=−48c = -48.

Answer: B

That is 1 of 24.

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All 24 diagrams

Common Questions

It comes up as an SAT nonlinear equations in one variable and systems of equations in two variables question. Two things to spot: you need a quadratic, and a sentence telling you how many solutions. That is a discriminant problem. Know the 3 cases: greater than 0 for 2 solutions, equal to 0 for 1 solution, and less than 0 for no solution. Then let Desmos solve it.

Read off a = -3, b = 24, c = c. Everything is already on one side. Exactly one solution is case ii: b^2 - 4ac = 0. 576 - 4(-3)(c) = 576 + 12c = 0, so c = -48.

No. The SAT reference sheet is twelve geometry formulas and three notes, and Discriminant is not one of them. It is one of the 24 things the test expects you to know without being given them. See what the reference sheet does cover at /blog/sat-math-reference-sheet.