QQuestion
If the roots of the equation x² − 22x + 105 = 0 are α and β, then find the value of 1/α + 1/β
✓Answer
For ax² + bx + c = 0,
sum of roots α + β = −b/a
and product αβ = c/a.
Here a = 1, b = −22, c = 105
⇒ α + β = 22 and αβ = 105.
So, 1/α + 1/β = (α + β) / (αβ) = 22 / 105
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