Answer:
[tex]x^2+7x+6=0[/tex]
Step-by-step explanation:
Assuming we want to find the quadratic equation whose roots are -6 and -1.
Then we can work backwards to find that equation.
Since -6 and -1 are roots of this equation, by the factor theorem x+6 an x+1 are also factors of the given equation.
[tex]x+6=0\:and\:x+1=0[/tex]
This implies that:
[tex](x+6)(x+1)=0[/tex]
We now expand to get:
[tex]x^2+6x+x+6=0[/tex]
Hence the required equation is [tex]x^2+7x+6=0[/tex]
