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Question
If α and β are the roots of the equation is 3x2 + x – 10 = 0, then the value of `1/α + 1/β` is ______.
Options
10
`- 1/10`
`1/10`
`1/3`
Solution
If α and β are the roots of the equation is 3x2 + x – 10 = 0, then the value of `1/α + 1/β` is `underline(1/10)`.
Explanation:
Given equation is, 3x2 + x – 10 = 0
Since α and β are the roots of given equation
∴ Sum of roots (α + β) = `(-b)/a = (-1)/3`
Product of roots (αβ) = `c/a = (-10)/3`
Now, `1/α + 1/β = (β + α)/(αβ)`Quadratic Equations
= `((-1)/3)/((-10)/3)`
= `(-1)/3 xx 3/(-10)`
= `1/10`
Thus, the value of `1/α + 1/β` is `1/10`.
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