Question

findthe zeroes of the quadratic polynomial x² - 13 x+42 and verify the relationship between zeores and coefficient

Answer 1

Heya !!!



P(X) = X² - 13X + 42



We try to split 42 in two parts such that their sum or Subtraction is 13 and their product will be 42.


Clearly,



-6 - 7 = -13


And,


-6 × -7 = 42



So,



X² - 13X + 42



X² - 6X - 7X + 42



X ( X - 6) -7 ( X - 6)



( X - 6) ( X - 7 ) = 0



(X -6) = 0 OR ( X -7) = 0



X = 6 OR X = 7




Relationship between the zeroes and Coefficient.




Sum of zeroes = Alpha + Beta = 6 +7 = 13/ 1 = Coefficient of X / Coefficient of X².



And,


Product of zeroes = 6 × 7 = 42 = Constant term / Coefficient of X².



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