When you solve t(t+1)(t-2)=0, is the solution {0, -1, -2}?
what is 0,-1, and +2
the solution set
To solve the equation t(t+1)(t-2) = 0, we can apply the zero-product property, which states that if a product of factors equals zero, then at least one of the factors must be zero.
So, we set each factor in the equation to zero and solve for t individually:
1) t = 0
2) t + 1 = 0
3) t - 2 = 0
For equation (2), we can solve for t by subtracting 1 from both sides:
t + 1 - 1 = 0 - 1
t = -1
Similarly, for equation (3), we can solve for t by adding 2 to both sides:
t - 2 + 2 = 0 + 2
t = 2
So, the solutions are t = 0, t = -1, and t = 2.
Therefore, the solution to the equation t(t+1)(t-2) = 0 is {0, -1, 2}, not {-2}.