Question

PLEASEEE HELP. Solve x^3-7x^2+6x-42=0

Answer 1

`x^(3) -7 x^(2) +6x-42=0`


`(x-7)` is a factor since it is a factor of -42 and 7 is a solution for f(x) to equal 0.


`(x-7)(a x^(2) +bx+c)=0`


`(x-7)( x^(2) +bx+6)=0`


`-7 x^(2) +b x^(2) =-7 x^(2)`


`-7+b=-7`


`b=0`


`(x-7)( x^(2) +6)=0`


`x-7=0`


`x^(2) +6=0`


`x=7` (only solution because you can't square root (-6))

Answer 2

factor by grouping

x^2(x-7) + 6(x-7) = 0 [took x^2 out of the first two and a 6 out of the last two]
(x-7)(x^2+6) = 0 [moved (x-7) out to the front]
x = -i sqrt(6) , i sqrt(6) , 7

only one real solution of x = 7