Answer:
The roots of the quadratic function [tex]f(x) = -x^{2}-6\cdot x -8[/tex] are [tex]x_{1} = -4[/tex] and [tex]x_{2} = -2[/tex].
Step-by-step explanation:
Let be [tex]f(x) = -x^{2}-6\cdot x -8[/tex], the function is now graphed by using a graphing tool and whose outcome is added below as attachment. After looking the image, the roots of the polynomial are [tex]x_{1} = -4[/tex] and [tex]x_{2} = -2[/tex], respectively. It can be also proved by algebraic means:
1) [tex]-x^{2}-6\cdot x -8=0[/tex] Given
2) [tex]-(x^{2}+6\cdot x+8 )= 0[/tex] Distributive property/ [tex]-(x) = -x[/tex]
3) [tex]-(x^{2} +4\cdot x +2\cdot x +8)= 0[/tex] Addition
4) [tex]-[x\cdot (x+4)+2\cdot (x+4)] = 0[/tex] Distributive property/Associative property
5) [tex]-(x+2)\cdot (x+4) = 0[/tex] Distributive property/Result
Which supports the graphic findings.
The roots of the quadratic function [tex]f(x) = -x^{2}-6\cdot x -8[/tex] are [tex]x_{1} = -4[/tex] and [tex]x_{2} = -2[/tex].
