Is this correct?

[Kim]

problem: 4xcubed-8xsquared-9x+18=0
my answers: x=2, x=3/2, x=-3/2

 

[matholympiad]

yes! you are correct.

the right answer is "x=2"

please reply if u dont understand how i got this

 

[Kim]

Why only x=2? is it because i need to check the other answers?

 

[Denis]

I'll bite: all 3 solutions are correct....why do you say only x=2 ?

x = 3/2:
4x^3 - 8x^2 - 9x + 18 = 0
4[(3/2)^3] - 8[(3/2)^2] - 9(3/2) + 18 = 0
27/2 - 18 - 27/2 + 18 = 0

similarly with x = -3/2

 

[soroban]

Hello, Kim!

I too see nothing wrong with your answers . . .

4x³ - 8x² - 9x + 18 = 0

My answers: x=2, x=3/2, x=-3/2

Factor "by grouping": .4x²(x - 2) - 9(x - 2) .= .0

Factor: . . . . . . . . . . . . . . . (x - 2)(4x² - 9) .= .0

Factor: . . . . . . . . . .(x - 2)(2x - 3)(2x + 3) .= .0

Therefore: . x .= .2, 3/2, -3/2