Question

find the zeroes of the quadratic polynomial xsquare-7x+10 and verify the relation between the zeroes and the co-efficients

Answer 1

Answer:

Step-by-step explanation:

We can find the zeroes by splitting the middle term

               x²-7x+10 = 0

              x²-5x-2x+10 = 0

             x(x-5) -2(x-5) = 0

             (x-5) (x-2) = 0

            x-5 = 0          x-2 = 0

           so,

                 x = 5,2

          Let α = 5 & β = 2

   Verification :

     Sum of zeroes = -coefficient of x

                                            coefficient of x²  

                             α+β   = -b

                                            a

                    5+2 =   -(-7)

                                     1

                     7 = 7

                LHS = RHS

Now,

       Product of zeroes = coefficient term

                                           coefficient of x²

                    αβ = c

                             a

                 5×2 = 10

                             2

                  10 = 10

              LHS = RHS

Hence, relation between the zeroes and the coefficients is verified.