Answer:
Question C:
Concept:
Define Discriminant
The discriminant can be positive, zero, or negative, and this determines how many solutions there are to the given quadratic equation. A positive discriminant indicates that the quadratic has two distinct real number solutions. A discriminant of zero indicates that the quadratic has a repeated real number solution.
The summary of the explanation is given below as
The equation in the question is given below as
[tex]x^2-10x+25=0[/tex]
The general form of a quadratic expression is given below as
[tex]ax^2+bx+c=0[/tex]
By comparing coefficients, we will have that
[tex]a=1,b=-10,c=25[/tex]
Hence,
The Discriminant of the equation will be
[tex]\begin{gathered} D=b^2-4ac \\ D=(-10)^2-4\times1\times25 \\ D=100-100 \\ D=0 \end{gathered}[/tex]
The roots of the equation will be calculated below as
[tex]\begin{gathered} x^2-10x+25=0 \\ two\text{ factors to give a product of 25 and sum of -10} \\ \end{gathered}[/tex][tex]\begin{gathered} x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ x=\frac{-(-10)\pm\sqrt{0}}{2\times1} \\ x=\frac{10}{2} \\ x=5 \end{gathered}[/tex]
Hence,
The number of roots is 0NE
The nature of the root is REAL
