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Question
If ∝ and β are the zeros of the polynomial f(x) = `6x^2 + x - 2 `find the value of `(∝/β+∝/β) `
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Solution
By using the relationship between the zeroes of the quadratic polynomial.
We have
Sum of zeroes=`(-("Coefficent of x"))/("Coefficient of" x^2)` and Product of zeroes = `"Constant term"/("Coefficient of" x^2)`
∴ 𝛼 + 𝛽=`-1/6` and 𝛼𝛽 =`-1/3`
Now, `∝/β+β/∝=(∝^2+β^2)/(∝β)`
`= (∝^2+β^2+2∝β-2∝β)/(∝β)`
`=((∝+β)^2-2∝β)/(∝β)`
`=((-1/6)^2-2(1/3))/(1/3)`
`=(1/36+2/3)/ (1/3)`
`=-25/12`
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