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Question
If α, β are the zeroes of the polynomial p(x) = 4x2 – 3x – 7, then `(1/α + 1/β)` is equal to ______.
Options
`7/3`
`(-7)/3`
`3/7`
`(-3)/7`
Solution
If α, β are the zeroes of the polynomial p(x) = 4x2 – 3x – 7, then `(1/α + 1/β)` is equal to `underlinebb((-3)/7)`.
Explanation:
p(x) = 4x2 – 3x – 7 = 0
α, β are the roots of above equation
∴ α + β = `- ("Coefficient of" x)/("Coefficient of" x^2)`
= `-((-3))/4`
= `3/4`
and αβ = `"Constant term"/("Coefficient of" x^2)`
= `(-7)/4`
Now, `1/α + 1/β`
= `(β + α)/(αβ)`
= `(α + β)/(αβ)`
= `(3/4)/((-7)/4)`
= `(-3)/7`
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