Question

Find a quadratic polynomial whoes zeros are -4and 3and verify the relationship between the zeros and coefficient

Answer 1

Heya !!



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.








Relationship between the zeroes and coefficient.



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


And,



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