Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Josettewould

  • 4 years ago

If an equation has a discriminant of zero, how many times will the graph touch the x–axis?

  • This Question is Closed
  1. JamesJ
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    If a quadratic equation has zero discriminent, how many distinct roots does it have?

  2. JamesJ
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    For example: \[ x^2 - 2x + 1 = 0 \] How many distinct roots does this equation have?

  3. JamesJ
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    quick ... talk to me

  4. JamesJ
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Notice the discriminent of that equation is zero because \[ b^2 - 4ax = (-2)^2 - 4(1)(1) = 4 - 4 = 0 \] Hence the equation only has one solution and that solution is \[ x = \frac{-b \pm \sqrt{b^2 - 4ax}}{2a} = \frac{2 \pm \sqrt{0}}{2} = \frac{2}{2} = 1 \]

  5. JamesJ
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    In general, quadratics with zero discriminent have how many distinct roots then? 0, 1 or 2?

  6. JamesJ
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    And here's the last piece of the puzzle. This is the graph of \[ y = x^2 - 2x + 1 \] Notice how many times it touches or crosses the x-axis.

  7. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy