Question

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

Answer 1

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.