Question

Find the zeroes following quadratic polynomial and verify the relationship between zeroes and coefficient 4x2-4x+1

Answer 1

Answer:

p(x) = 4x^2 - 4x +1 (ax^2 + bx + c)[here a = 4, b = -4, c = 1]

4x^2 - 2x - 2x + 1

2x(2x-1) -1(2x-1)

(2x-1)(2x-1)

x = 1/2

or x = 1/2

let α be 1/2

and β be 1/2

sum of zeroes = α+β

                        =1/2 +1/2

                        = 1

but sum of zeroes = -b/a

                              = -(-4)/4

                              = 1

hence -b/a = α+β

product of zeroes = α*β

                              = 1/2 * 1/2

                              = 1/4

   

but product of zeroes = c/a

                                     = 1/4

hence verified  

Step-by-step explanation: