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Josettewould

  • 2 years ago

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

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  1. JamesJ
    • 2 years ago
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    If a quadratic equation has zero discriminent, how many distinct roots does it have?

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

  3. JamesJ
    • 2 years ago
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    quick ... talk to me

  4. JamesJ
    • 2 years ago
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    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
    • 2 years ago
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    In general, quadratics with zero discriminent have how many distinct roots then? 0, 1 or 2?

  6. JamesJ
    • 2 years ago
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    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.

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