SAT Math Multiple Choice Question 324: Answer and Explanation

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Test Information

Question: 324

9. How many real values of x satisfy the quadratic equation 9x2 – 12x + 4 = 0?

  • A. 0
  • B. 1
  • C. 2
  • D. 4

Correct Answer: B

Explanation:

B

Difficulty: Medium

Category: Passport to Advanced Math / Quadratics

Strategic Advice: A quadratic equation can have zero, one, or two real solutions. There are several ways to determine exactly how many. You could graph the equation and see how many times it crosses the x-axis; you could calculate the discriminant (the value under the square root in the quadratic formula); or you could try to factor the equation. Use whichever method gets you to the answer the quickest.

Getting to the Answer: Notice that the first and last terms in the equation are perfect squares-this is a hint that it could be a perfect square trinomial, which it is. The factored form of the equation is (3x - 2)(3x - 2). Both factors are the same, so there is only one real value, that satisfies the equation.

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