Given:
Polynomial [tex]x^2+6x+20[/tex]
To find:
The equivalent polynomial.
Solution:
[tex]x^2+6x+20=0[/tex]
a = 1, b = 6, c = 20
Using quadratic formula:
[tex]$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]
[tex]$x=\frac{-6 \pm \sqrt{6^{2}-4 \cdot 1 \cdot 20}}{2 \cdot 1}[/tex]
[tex]$x=\frac {-6 \pm \sqrt{-44}}{2}[/tex]
44 can be written as 11 × 4 = 11 × 2²
[tex]$x= \frac {-6 \pm \sqrt{-11 \times 2^2}}{2}[/tex]
[tex]$x= \frac {-6 \pm2 \sqrt{-11 }}{2}[/tex]
[tex]$x =\frac{2(-3 \pm i \sqrt{11})}{2}[/tex]
Cancel the common factor 2.
[tex]$x =-3 \pm i \sqrt{11}[/tex]
[tex]$x =-3 + i \sqrt{11}[/tex], [tex]$x =-3 - i \sqrt{11}[/tex]
Convert into factors.
[tex]$x -(-3 + i \sqrt{11})=0[/tex], [tex]$x -(-3 - i \sqrt{11})=0[/tex]
[tex]$x + (3 - i \sqrt{11})=0[/tex], [tex]$x + (3 + i \sqrt{11})=0[/tex]
[tex]$(x + (3 - i \sqrt{11}))(x + (3 + i \sqrt{11}))[/tex]
Interchange their positions.
[tex]$(x + (3 + i \sqrt{11}))(x + (3 - i \sqrt{11}))[/tex]
Therefore option B is the correct answer.
The equivalent polynomial is [tex]$(x + (3 + i \sqrt{11}))(x + (3 - i \sqrt{11}))[/tex].
