Question

Find the quadratic polynomial whose zeroes are -4 and 3 and verify the relationship between the zeroes and the coefficients.

Answer 1

Let Alpha = -4 and Beta = 3.



Sum of zeroes = Alpha + Beta = -4 + 3 = -1


And,


Product of zeroes = Alpha × Beta = -4 × 3 = -12.



Therefore,


Required quadratic polynomial = X² - ( Sum of zeroes)X + Product of zeroes



=> X² - ( -1 ) X + ( -12 )



=> X² + X - 12.



_____________________________



P ( X ) = X² + X - 12



Here,

A = Coefficient of X² = 1


B = Coefficient of X = 1

And,


C = Constant term = -12







Relationship between the zeroes and Coefficients.




Sum of zeroes = Alpha + Beta = -4 + 3 = -1/1 = - ( Coefficient of X ) / ( Coefficient of X²).


And,

Product of zeroes = Alpha × Beta = -4 × 3 = -12/1 = Constant term / Coefficient of X².

Answer 2

Here is your answer in the attached photo