determine the nature of the solutions of the equation. Two real solutions, two imaginary solutions, or one real solution.
2t^2-4t=0
Here, discriminant = (-4)^2 = 16
Hence, discriminant is positive and greater than 0
Therefore, there are two real solutions of the given equation
To determine the nature of the solutions of the equation 2t^2 - 4t = 0, we need to solve the equation.
Step 1: Rewrite the equation in standard form: 2t^2 - 4t = 0
Step 2: Factor out the common term t from both terms on the left side of the equation: t(2t - 4) = 0
Step 3: Apply the zero product property, which states that if a product of factors equals zero, then at least one of the factors must be equal to zero.
So, we set each factor equal to zero and solve for t:
t = 0
2t - 4 = 0
Solving the second equation, we add 4 to both sides of the equation:
2t = 4
Then, divide both sides by 2:
t = 2
Step 4: Now, we have found two solutions, t = 0 and t = 2.
As there are two distinct real solutions, the nature of the solutions of the equation 2t^2 - 4t = 0 is two real solutions.