Question

-3x^{2}-21x-54 what are the zeros? (Solutions)

Answer 1

the only way to solve if it is equal to something
assuming that the teacher wanted you to make it equal to zero do
0=-3x^2-21x-54

remember if we can do
xy=0 then assume x and y=0

so factor

0=-3x^2-21x-54
undistribute the -3
0=-3(x^2+7x+18)
remember 0 times anything=0 so
x^2+7x+18 must equal zero
use quadratice formula which is

if you have
ax^2+bx+c=0 then
x=
`\frac{-b+/- \sqrt{b^(2)-4ac} }{2a}`

x^2+7x+18
a=1
b=7
c=18

x=
`\frac{-7+/- \sqrt{7^(2)-4(1)(18)} }{2(1)}`
x=
`(-7+/- √(49-72) )/(2)`
x=
`(-7+/- √(-23) )/(2)`
i=√-1
x=
`(-7+/- i√(23) )/(2)`



the zerose would be
x=
`(-7+ i√(23) )/(2)` or
`(-7- i√(23) )/(2)`