How many polynomials are there having 9 and -7 as zeroes - Maths - Polynomials

Question

How many polynomials are there having 9 and -7 as zeroes

Anuradha Sharma · Accepted Answer

From the given zeros, sum of roots = 9-7=2and product of roots = 9×-7=-63Now forming a qudratic equation, x2-sum of rootsx+product of roots =0x2-2x-63=0So f x=0 or x2-2x-63=0 is a single equation but there are infinite polynomial because, polynomial is x2-2x-63 or x-9x+7But afx=ax-9x+7 is also having same root as that of x-9x+7
SO for a given roots the equation is one but polynomials are infinite