Question

solve this quadratic equation by factorization and check the solutions

9x^2 - 27x + 14 = 0

Answer 1

Given Equation is 9x^2 - 27x + 14 = 0

= > 9x^2 - 21x - 6x + 14 = 0

= > 3x(3x - 7) - 2(3x - 7) = 0

= > (3x - 2)(3x - 7) = 0


(1)

3x - 2 = 0

= > 3x = 2

= > x = (2/3).



(2) 

3x - 7 = 0

= > 3x = 7

= > x = (7/3).

Verification:

When x = (2/3):

= > 9(2/3)^2 - 27(2/3) + 14

= > 9(4/9) - 18 + 14

= > 4 - 4

= > 0.



when x = (7/3):

= > 9(7/3)^2 - 27(7/3) + 14

= > 49 - 63 + 14

= > 49 - 49

= > 0.




Hope this helps!

Answer 2

  9x^2 - 21x - 6x + 14 = 0
= 3x(3x - 7) - 2(3x - 7) = 0
= (3x - 2)(3x - 7) = 0
= x = 2/3 , 7/3


-b/a = 27/9 = 3   Also, 2/3 + 7/3 = 3
c/a  = 14/9         Also, 2/3 x 7/3 = 14/9