Question

Find the polynomial expression for following of zeros 2and -3

Answer 1

In order to have a zero of -2 it must have a factor of (x+2) so that when (x+2) is set = 0, the result will be x = -2 So suppose the other factor is, say, (3x-4). You could make up any binomial for the second factor. I just arbitrarily picked (3x-4). Then multiply it by (x+2): (3x-4)(x+2) FOIL it out: 3x²+6x-4x-8 Combine like terms: 3x²+2x-8 f(x) = 3x²+2x-8 is one possibility. There are many others. Edwin

Answer 2

The zeroes are 2 and -3.
Sum of zeroes = α + β = -b/a
                        = 2+(-3)  = -b/a
                        = -1 = -b/a
                        = -1/1 =  -b/a
           Therefore -b = -1  
                             b = 1
                             a = 1 

Product of zeroes=  α*β = c/a
                            =  2*(-3) =c/a
                            = -6 = c/a    
                            = -6/1 = c/a
      Therefore c= -6 and a= 1
 
a=1, b=1 and c=-6

Polynomial = ax^2 + bx + c
                   = x^2 + x -6 (after putting values of a, b and c)

Hence our polynomial is x^2 + x -6.