Question

find the zeros of the polynomial and verify its relationship between the zeros and coefficients .
i) p(x) equal to
${x }^{2} - 7x + 12$

Answer 1

X² - 7X + 12


X² - 4X - 3X + 12




X ( X - 4 ) - 3 ( X - 4 )



( X - 4 ) ( X - 3 ) = 0


( X - 4 ) = 0 OR ( X - 3 ) = 0



X = 4 or X = 3.




Hence,

4 and 3 are the two zeroes of the given quadratic polynomial X² - 7X + 12.




Let Alpha = 4 and Beta = 3.




Relationship between the zeroes and Coefficient.



Sum of zeroes = Alpha + Beta = 4 + 3 = 7 = - ( Coefficient of X ) / ( Coefficient of X² ).



And,


Product of zeroes = Alpha × Beta = 4 × 3 = 12 = ( Constant term / Coefficient of X² ).

Answer 2

x^2-7x+12
x*x-(4+3)x+12
x*x-4x-3x+12
x(x-4)-3(x-4)
(x-3) (x-4) Answer