Question
If α and β are the zeros of the quadratic polynomial f(x) = 6x2 + x − 2, find the value of `alpha/beta+beta/alpha`
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`
Is there an error in this question or solution?
Solution If α And β Are the Zeros of the Quadratic Polynomial F(X) = 6x2 + X − 2, Find the Value of `Alpha/Beta+Beta/Alpha` Concept: Relationship Between Zeroes and Coefficients of a Polynomial.
