Complete the statements.

Accepted Solution

Answer:Graph B has one real root.Graph A has a negative discriminantGraph 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]_____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.