Will the solutions to the equation 12x^2-5x-2=0 be positive or negative and how would you know without solving the equation completely?

Hey there! Let's look at this equation differently!  

ax^2-bx-c=0

we know that the factored form will have different signs like this

(dx-f)(ex+g)
ex+g=0
ex=-g

therefor there is a positive and negative answer (2 roots total)

I hope this helps! 

The answer is

1.   an exact solution requires a radical solution - no decimal approximation.2. (a)4x^3 = 756x^3 = 756/4 = 189x =   cube root of 189 =   5.74   to nearest hundredth answer(b)   189 = 3*3*3*7   so we can write the cube root of 189 as 3∛7 answerchecking (a) 4*(5.74^3 =   756.48   which is very close(b)   4* ((3∛3)^3   = 4*189   = 756   - spot on! 3. i would use solution b because the original question asked for an exact solution.