2. Why does the equation 3x2 - 30 = 3 have two solutions but the equation 3x2 + 30 = 3 has no solution?
what are some different values for x.
The equation 3x2 - 30 = 3 has two solutions because it can be factored as 3(x2 - 10) = 3, which simplifies to x2 - 10 = 1. This equation can then be further simplified to x2 = 11, which has two solutions: x = √11 and x = -√11.
On the other hand, the equation 3x2 + 30 = 3 cannot be factored in the same way as it does not simplify down to a quadratic equation with real solutions. This equation simplifies to 3x2 = -27, which has no real solution as the square of any real number is always non-negative.
Some different values for x in the first equation (3x2 - 30 = 3) include x = √11, x = -√11, and any real number that satisfies the equation x2 = 11, as these are the solutions to the equation.