Answer:
The discriminant equals zero.
Explanation:
The standard form of a quadratic equation is
ax² + bx + c = 0
The solution is the familiar quadratic formula
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
The term b² -4ac is the discriminant (D).
D tells you the number of roots.
If D = 0, the solution to the equation becomes
[tex]x = \frac{-b\pm\sqrt{0}}{2a}[/tex]
[tex]x = \frac{-b}{2a}[/tex]
If D = 0, there is exactly one zero.
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Example:
Find the zeroes of
f(x) = x² - 2x + 1
[tex]x = \frac{2 \pm \sqrt{(-2)^{2} - 4(1)(1)}}{2(1)}[/tex]
[tex]x = \frac{2 \pm\sqrt{4 - 4}}{2}[/tex]
[tex]x = \frac{2 \pm\sqrt{0}}{2}[/tex]
[tex]x = \frac{2 \pm 0}{2}[/tex]
[tex]x = \frac{2}{2}[/tex]
x = 1
The graph is a parabola with its vertex touching the x-axis at x = 1.
