Question

If α and β are the zeroes of the polynomial x² + x − 2, then find the value of `alpha/beta+beta/alpha`

Answer 1

Step 1: Use Sum and Product of Roots

Sum of roots: `alpha+beta = ("−coefficient of x")/("coefficient of"  x^2)`

Product of roots: `alpha beta = ("constant term")/("coefficient of"  x^2) = -2/1 = -2`

Step 2: Find `alpha/beta + beta/alpha`

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

α² + β² = (α + β)² − 2αβ

Substituting known values:

α² + β² = (−1) 2 − 2(−2)

= 1 + 4 = 5

`alpha/beta + beta/alpha = 5/-2`

`= -5/2`