Question

How do you find all zeros of the function `x² + 24 = –11x`?

Answer 1

`x=-3color(white)("XXX")andcolor(white)("XXX")x=-8`

Explanation:

Re-writing the given equation as
`color(white)("XXX")x^2+11x+24=0`
and remembering that
`color(white)("XXX") (x+a)(x+b)=x^2+(a+b)x+ab`

We are looking for two values, `a` and `b` such that
`color(white)("XXX")a+b=11` and
`color(white)("XXX")ab=24`

with a bit of thought we come up with the pair `3` and `8`

So we can factor:
`color(white)("XXX")(x+3)(x+8)=0`

which implies either `x=-3` or `x=-8`

Answer 2

x=-8 or x=-3

Explanation:

First you get the equivalent equation
`x^2+11x+24=0`
then you solve
`x=-11/2+-sqrt(11^2-4(24))/2`
`x=-11/2+-sqrt(25)/2`
`x=-11/2+-5/2`
so x=-8 or x=-3