Zeros
Find the
of the quodric
polynomial 4xspuare-4x+1and verify the
relationship between zeros
and its

October 17, 2021

By Athena

1 thought on “Zeros<br />Find the<br />of the quodric<br />polynomial 4xspuare-4x+1and verify the<br />relationship between zeros<br />and its<b”

1. Given :

   Give a quadratic equation 4x²-4x+1.

   To find :

   We have to find their zeroes and verify the relationship between the zeroes.

   Solution :

   For knowing the zeroes of the polynomial 4x²-4x+1, we’ll split it’s middle term :

   • 4x²-2x-2x+1
   • 2x (2x-1) – 1(2x-1)
   • (2x-1) (2x-1)
   • x = 1/2

   Therefore, x=1/2 is the zero of the quadratic equation 4x²-4x+1.

   Now, verifying the relationship between the zeroes :

   • Product of zeroes = c/a
   • Sum of zeroes = -b/a

   When we compare ax²+bx+c [a≠0] to 4x²-4x+1, we get :

   • a = 4
   • b = -4
   • c = 1

   Here,

   • Product of zeroes = c/a
   • 1/2(1/2) = 1/4
   • 1/4 = 1/4
   • Sum of zeroes = -b/a
   • 1/2+1/2 = -(-4)/4
   • 2/2 = 4/4
   • 1 = 1
   • LHS = RHS

   Hence, verified!

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