Practice Quiz

SAT Math

Category - Algebra and Functions

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What is the number of real solutions of x^4 − 1 = 0?
  1. 0
  2. 1
  3. 2
  4. 3
  5. 4
Explanation
Answer: C - The number of real solutions is 2. Use x^2 − y^2 = (x − y)(x + y)
x^4 − 1 = 0
(x^2 )^2 − 1^2 = 0
(x^2 − 1)(x^2 + 1) = 0
x^2 − 1 = 0
x^2 = 1
x = ±√1 = ±1
x^2 + 1 = 0
x^2 = − 1
x = ±√( − 1) = ±i

So, there are two real solutions.
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