Question

Find the real root of x^3+4x^2-10x+12, use synthetic division and the quadratic formula to find the other 2 roots

Answer 1

you can find 1 root by factor, then the opposite of your answer will also be a root

Answer 2

How would I factor this out? x(x^2 +4x-10+12)?

Answer 3

you can graph the function to get an idea of what the roots are

then verify with synthetic division

Answer 4

I know I can graph it(I just did it) but I'm pretty sure my teacher wants us to find the
real root algebraically

Answer 5

well then you use rational root thm, possible roots are +-1,+-2,+-3,+-4,+-6,+-12

Answer 6

And then I input them and the equation has to equal to zero, correct?

Answer 7

I input a number, i mean*

Answer 8

right...the remainder will be zero if it is a factor

Answer 9

When I found a factor is -6 on the calculator, I input into the equation and it didn't equal to zero. I think it is something I am doing wrong but I don't know what it is

Answer 10

hmm no -6 should work

-6 | 1 4 -10 12
-6 12 -12
----------------
1 -2 2 0

Answer 11

(x+6)(x^2-2x+2)

Answer 12

OH! So I pick a number and I don't input into the equation, I use synthetic division to get it to equal to zero?

Answer 13

and then I use quadratic equation for x^2-2x+2 to get the last 2 factors

Answer 14

well either one actually....but it says to use synthetic division

check your calculator again, you should get 0

Answer 15

when I did synthetic division I got the same answer as you. I'm probably doing something algebraically wrong when I input the number in the equation.

Answer 16

(-6)^3 +4(-6)^2 -10(-6) +12 = 0

-216 +4(36) +60+12 = 0

-216 +144 +72 = 0
-216 + 216 = 0

Answer 17

then after using quadratic formula you should get: 1 +- i for other 2 roots

Answer 18

Yep!

Answer 19

Thank you so much!

Answer 20

yw :)