anonymous
  • anonymous
If an equation has a discriminant of zero, how many times will the graph touch the x–axis?
Mathematics
chestercat
  • chestercat
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JamesJ
  • JamesJ
If a quadratic equation has zero discriminent, how many distinct roots does it have?
JamesJ
  • JamesJ
For example: \[ x^2 - 2x + 1 = 0 \] How many distinct roots does this equation have?
JamesJ
  • JamesJ
quick ... talk to me

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JamesJ
  • JamesJ
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 \[ x = \frac{-b \pm \sqrt{b^2 - 4ax}}{2a} = \frac{2 \pm \sqrt{0}}{2} = \frac{2}{2} = 1 \]
JamesJ
  • JamesJ
In general, quadratics with zero discriminent have how many distinct roots then? 0, 1 or 2?
JamesJ
  • JamesJ
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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