Will the solutions to the equation 12x2-5x-2=0 be positive or negative and how would you know without solving the equation completely?

For this case we have the following equation:

12x2-5x-2 = 0

Using the resolver we have:

x = ( - b + / - root (b ^ 2 - 4 * a * c)) / (2 * a)

Substituting values we have:

x = ( - ( - 5) + / - root (( - 5) ^ 2 - 4 * 12 * ( - 2))) / (2 * 12)

Rewriting:

x = (5 + / - root (25 + 96))) / (2 * 12)

x = (5 + / - root (121))) / (2 * 12)

x = (5 + / - 11) / (2 * 12)

Answer:

One root is positive and another is negative.