Chapter 11.6, Problem 26STP

To determine

To find: Thecorrect option for the given geometry.

Answer to Problem 26STP

The correct option for the given geometry is $\text{J}$ .

Explanation of Solution

Given information:

The given equation is,

  $x^2-10x+c=0$

The roots of the given equation are $\left(5+i\right)\text{and }\left(5-i\right)$ .

Concept used:

The standard equation for the linear function cab be written as,

  $y=mx+b$

Here, the slope of the graph is $m$ and the $y$ -intercept is $b$ .

The quadratic equation is calculated from the roots as,

  $\begin{array}{l}\left(x-\left(5+i\right)\right)\left(x-\left(5-i\right)\right)=0\\ x\left(x-\left(5-i\right)\right)-\left(5+i\right)\left(x-\left(5-i\right)\right)=0\\ x^2-\left(5-i\right)x-\left(5+i\right)x+\left(5^2-i^2\right)=0\\ x^2-10x+26=0\end{array}$

Comparing the given equation to obtain,

  $c=26$

Thus, the correct option for the given geometry is $\text{J}$ .