Answer:
C. The discriminant is negative, so there are no solutions.
Step-by-step explanation:
We see that the given figure is a graph of a parabola.
The equation of the given parabola is [tex]y=(x-3)^{2}+1[/tex].
Simplifying the equation in quadratic form, we get,
The equation is [tex]y=(x-3)^{2}+1[/tex] i.e. [tex]y=x^{2}+9-6x+1[/tex] i.e. [tex]y=x^{2}-6x+10[/tex].
We know that the discriminant of a quadratic equation [tex]ax^{2}+bx+c=0[/tex] is given by [tex]D=b^{2}-4ac[/tex]
So, from the equation [tex]x^{2}-6x+10=0[/tex], we have,
a = 1, b = -6 and c = 10
Thus, the discriminant is [tex]D=(-6)^{2}-4\times 1\times 10[/tex]
i.e. [tex]D=36-40[/tex]
i.e. [tex]D=-4[/tex]
So, the discriminant is -4 i.e. negative.
Hence, as the discriminant is negative, there are no solutions.
