Find the zeros of the quadratic polynomial p(x) = 4x² – 4x + 1 and verify the relationship between the
zeros and their coeffi

2 thoughts on “Find the zeros of the quadratic polynomial p(x) = 4x² – 4x + 1 and verify the relationship between the<br />zeros and their coeffi”

1. Answer:

   Both roots are [tex]\frac{1}{2}[/tex]

   Step-by-step explanation:

   4x² – 4x +1 = 0 a= 4; b= -4; c= 1

   4x² – 2x – 2x + 1 =0

   2x(2x – 1) – 1(2x -1) =0

   (2x – 1)(2x – 1) = 0

   So, on solving we will get x =1/2 ; x = 1/2

   Zeroes are,

   [tex]\alpha[/tex] = [tex]\frac{1}{2}[/tex]

   [tex]\beta[/tex] = [tex]\frac{1}{2}[/tex]

   [tex]\alpha[/tex] + [tex]\beta[/tex] =[tex]\frac{-b}{a}[/tex]

   [tex]\frac{1}{2}[/tex] + [tex]\frac{1}{2}[/tex] = [tex]\frac{-(-4)}{4}[/tex]

   1 = [tex]\frac{4}{4}[/tex]

   1 = 1

   Hence Proved

   [tex]\alpha[/tex] x [tex]\beta[/tex] =[tex]\frac{c}{a}[/tex]

   [tex]\frac{1}{2}[/tex] x [tex]\frac{1}{2}[/tex] = [tex]\frac{1}{4}[/tex]

   [tex]\frac{1}{4}[/tex] = [tex]\frac{1}{4}[/tex]

   Hence Proved

   Hope this helps

   Pls make me brainliest

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2. Answer:

   a =4, b =-4, c=1

   sum of zero = -b/a

   =1

   product of zero = c/a

   =1/4

   now verification :

   4x²-4x+1

   4x²-2x-2x+1

   so by solving this we get two values of x that is

   x=1/2 and x =1/2

   so verification of sum of zeroes = 1/2+1/2=2/2=1

   now verification of product of zeroes = 1/2*1/2=1/4

   verified

   Reply