9t^2-3t=0. Solve using quadratic formula
if the constant is missing, there is no need to use the formula, since the equation will always factor
9t^2 - 3t = 0
3t(3t-1) = 0
t = 0 or t = 1/3
if you insist ....
a = 9, b = -3, c = 0
x = (3 ± √(9-0)/18
= (3±3)/18
= 1/3 or 0
To solve the quadratic equation 9t^2 - 3t = 0 using the quadratic formula, we need to identify the values of a, b, and c in the equation ax^2 + bx + c = 0.
In this case, a = 9, b = -3, and c = 0.
The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions can be found using the formula:
x = (-b ± √(b^2 - 4ac))/(2a)
Now, let's substitute the values of a, b, and c:
t = (-(-3) ± √((-3)^2 - 4(9)(0)))/(2(9))
Simplifying further:
t = (3 ± √(9 - 0))/(18)
t = (3 ± √9)/(18)
t = (3 ± 3)/(18)
This gives us two possible solutions:
1) t = (3 + 3)/(18) = 6/18 = 1/3
2) t = (3 - 3)/(18) = 0/18 = 0
Therefore, the solutions to the equation 9t^2 - 3t = 0 are t = 1/3 and t = 0.