Question

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

Answer 1

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

Answer 2

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

Answer 3

quick ... talk to me

Answer 4

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

Answer 5

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

Answer 6

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.