Question

Let `r` be the root of the equation `x^2 + 2x + 6`.What is the value of `(r+2)(r+3)(r+4)(r+5)`?

Answer 1

Please see the handscript below ; `-126`

Explanation:

Hope this helps

Answer 2

`-126`

Explanation:

The equationmust be
`x^2+2x+6=color(red)0`
If r is one of the root of this equation,then
`r^2+2r+6=0rArrcolor(red)(r^2+2r)=-6,and color(red)(r^2)=-2r-6`
Now, `(r+2)(r+3)(r+4)(r+5)=(color(red)(r^2)+5r+6)(color(red)(r^2)+9r+20)=(-2r-6+5r+6)(-2r-6+9r+20)` `=(3r)(7r+14)=21r(r+2)=21(color(red)(r^2+2r))=21(-6)`
`=-126`