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The Square Root Property quiz

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이 집합의 용어 (15)

  • What is the square root property used for when solving quadratic equations?
    It is used to solve equations where a squared term is isolated by taking the square root of both sides, yielding both positive and negative solutions.
  • If x² = 16, what are the solutions for x using the square root property?
    x = 4 and x = -4.
  • Why do we include both positive and negative roots when solving x² = k?
    Because both (positive root)² and (negative root)² equal k.
  • What should you do first when solving 4x² - 8 = 0 using the square root property?
    Add 8 to both sides to isolate the squared term.
  • After isolating x² = 2, what are the solutions for x?
    x = √2 and x = -√2.
  • How do you solve (x + 1)² = 4 using the square root property?
    Take the square root of both sides to get x + 1 = ±2, then solve for x.
  • What are the final solutions for x in the equation (x + 1)² = 4?
    x = 1 and x = -3.
  • When can you use the square root property to solve a quadratic equation?
    When a squared term is isolated and set equal to a constant.
  • What happens if you get a negative number under the square root when using the square root property?
    The solutions are imaginary and involve the imaginary unit i.
  • How do you simplify √(-16)?
    Rewrite it as √16 × √(-1), which is 4i.
  • What are the solutions to x² = -16?
    x = 4i and x = -4i.
  • Why is it important to check your solutions by plugging them back into the original equation?
    To verify that the solutions make the original equation true.
  • What type of quadratic equations is the square root property especially useful for?
    Equations missing the linear (bx) term or those written as a binomial squared.
  • What is the imaginary unit i defined as?
    i is defined as the square root of -1.
  • What is the first step in solving 2x² + 32 = 0 using the square root property?
    Subtract 32 from both sides to begin isolating the squared term.