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## Josettewould Group Title If an equation has a discriminant of zero, how many times will the graph touch the x–axis? 2 years ago 2 years ago

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1. JamesJ

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

2. JamesJ

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

3. JamesJ

quick ... talk to me

4. 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 $x = \frac{-b \pm \sqrt{b^2 - 4ax}}{2a} = \frac{2 \pm \sqrt{0}}{2} = \frac{2}{2} = 1$

5. JamesJ

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

6. 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.