Question

find the zeros of the quadratic polynomial and verify the relationship between the zeros and coefficient of 6 x square subtract 3 subtract 7x

Answer 1

Heya !!!



6X² - 3 - 7X


6X² - 7X - 3



Here,


6 × -3 = -18


We try to split 18 into two parts such that their sum Or subtraction is 7 and Product is -18.



Clearly,




9 - 2 = 7

And,

9 × -2 = -18


So,


6X² - 7X - 3

6X² - ( 9- 2)X - 3 = 0

6X² -9X +2X - 3


3X ( 2X - 3) +1 ( 2X -3) = 0


( 2X - 3) ( 3X +1) = 0


(2X -3) = 0 OR ( 3X +1) = 0



X = 3/2 OR X = -1/3




Relationship between the zeroes and Coefficient.




Sum of zeroes = 3/2 - 1/3 = 9-2/6 = 7/6 = - (Coefficient of X) / Coefficient of X².



And,


Product of zeroes = 3/2 × -1/3 = -3 / 6 = Constant term / Coefficient of X².



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