Section D Section D Checkpoint

Problem 1

Use the quadratic formula to find exact solutions to these equations.

x=-b±b2−4ac2ax = \dfrac{\text-b \pm \sqrt{b^2-4ac}} { 2a}

  1. 3x2−2x−1=03x^2 - 2x - 1 = 0
  2. x2+4x=1x^2 + 4x = 1
Show Solution
Solution
  1. x=-13x = \text{-}\frac{1}{3} and x=1x = 1
  2. x=-2±5x = \text{-}2 \pm \sqrt{5}
Show Sample Response
Sample Response
  1. x=-13x = \text{-}\frac{1}{3} and x=1x = 1
  2. x=-2±5x = \text{-}2 \pm \sqrt{5}

Problem 2

Classify each value as rational or irrational. Explain your reasoning.

  1. 292 \sqrt{9}
  2. 3−103 - \sqrt{10}
  3. 1⋅2\sqrt{1} \boldcdot \sqrt{2}
Show Solution
Solution
  1. Rational. Sample reasoning: 29=2⋅3=62 \sqrt{9} = 2\boldcdot 3 = 6
  2. Irrational. Sample reasoning: The sum of a rational number and an irrational number is irrational.
  3. Irrational. Sample reasoning: The product of a nonzero rational number and an irrational number is irrational.
Show Sample Response
Sample Response
  1. Rational. Sample reasoning: 29=2⋅3=62 \sqrt{9} = 2\boldcdot 3 = 6
  2. Irrational. Sample reasoning: The sum of a rational number and an irrational number is irrational.
  3. Irrational. Sample reasoning: The product of a nonzero rational number and an irrational number is irrational.