If α and β are the roots of the equation 3x2 + 5x - 2 = 0, find the value of 1/α + 1/β
Answer Details
We know that if α and β are the roots of the quadratic equation ax^2 + bx + c = 0, then α + β = -b/a and α × β = c/a.
In this equation, 3x^2 + 5x - 2 = 0, we have a = 3, b = 5, and c = -2.
So, α + β = -b/a = -5/3
And, α × β = c/a = -2/3
We need to find the value of 1/α + 1/β = (α + β)/(α × β) = (-5/3) / (-2/3) = 5/2.
Therefore, the value of 1/α + 1/β is 5/2.