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If α And β Are the Zeros of the Quadratic Polynomial F(X) = 6x2 + X − 2, Find the Value of `Alpha/Beta+Beta/Alpha` - Mathematics

If α and β are the zeros of the quadratic polynomial f(x) = 6x2 + x − 2, find the value of `alpha/beta+beta/alpha`

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Solution

f(x) = 6𝑥2 − 𝑥 − 2

Since α and β are the zeroes of the given polynomial

∴ Sum of zeroes [α + β] `=(-1)/6`

Product of zeroes `(alphabeta)=(-1)/3`

`=alpha/beta+beta/alpha=(alpha^2+beta^2)/(alphabeta)=((alpha+beta)^2-2alphabeta)/(alphabeta)`

`=((1/6)^2-2xx((-1)/3))/(-1/3)`

`=(1/6-2/3)/(-1/3)`

`=((1+24)/36)/(-1/3)`

`=(25/36)/(-1/3)`

`=-25/12`

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APPEARS IN

RD Sharma Class 10 Maths
Chapter 2 Polynomials
Exercise 21.00 | Q 3 | Page 34
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