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 2 years ago
If an equation has a discriminant of zero, how many times will the graph touch the x–axis?
 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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JamesJ
 2 years ago
Best ResponseYou've already chosen the best response.1If a quadratic equation has zero discriminent, how many distinct roots does it have?

JamesJ
 2 years ago
Best ResponseYou've already chosen the best response.1For example: \[ x^2  2x + 1 = 0 \] How many distinct roots does this equation have?

JamesJ
 2 years ago
Best ResponseYou've already chosen the best response.1Notice 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 \[ x = \frac{b \pm \sqrt{b^2  4ax}}{2a} = \frac{2 \pm \sqrt{0}}{2} = \frac{2}{2} = 1 \]

JamesJ
 2 years ago
Best ResponseYou've already chosen the best response.1In general, quadratics with zero discriminent have how many distinct roots then? 0, 1 or 2?

JamesJ
 2 years ago
Best ResponseYou've already chosen the best response.1And 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 xaxis.
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