Answer:
- Graph B has one real root.
- Graph A has a negative discriminant
- Graph C has an equation with the coefficients a=1, b=4, c=-2.
Step-by-step explanation:
The number of real roots is the number of places where the graph intersects the x-axis. When the discriminant is negative, there are none. Graph A does not cross the x-axis, so has a negative discriminant.
Graph B intersects the x-axis at one point, so it has one real root.
Graph C has two real roots, consistent with the positive discriminant associated with the given coefficients:
[tex]d=b^2-4ac=4^2-4(1)(-2)=16+8=24[/tex]
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For quadratic ...
[tex]y=ax^2+bx+c[/tex]
the discriminant is ...
[tex]d=b^2-4ac[/tex]
and the roots are ...
[tex]x=\dfrac{-b\pm\sqrt{d}}{2a}[/tex]
Then the roots are only real when the discriminant is non-negative. The square root function will not give real values for a negative argument.
