If α and β are the roots of the quadratic equation 3x^2-4x+7=0 find α-β

Answer 1

To solve this problem, we first need to find the values of α and β, which are the roots of the quadratic equation. We can do this by using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = 3, b = -4, and c = 7. Plugging these values into the formula yields:

α = (4 + √(-44)) / 6 ≈ 0.667 + 1.232i
β = (4 - √(-44)) / 6 ≈ 0.667 - 1.232i

Therefore, α - β = (0.667 + 1.232i) - (0.667 - 1.232i) = 2.464i.

So, the answer to the question is α - β = 2.464i.