Question

If alpha and beta are the zeroes of the polynomial p(x) = x
2
– mx + n, then find the value of
Alpha upon beta plus beta upon alpha

Answer 1

Given :  alpha and beta are the zeroes of the polynomial  p(x) = x² – mx + n

To find : α/β  + β/α

Solution:

alpha and beta are the zeroes of the polynomial  

p(x) = x² – mx + n

α + β  = -(-m)/1  = m

αβ  = n  

α/β  + β/α

= (α²  + β²)/αβ

= ( (α + β)²  - 2αβ ) / αβ

= ( m² - 2n)/n

=  m²/n - 2

α/β  + β/α  = m²/n - 2

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