Find the zeros of the quadratic polynomials 4x2 – 4x + 1 and verif

1.	Find the zeros of the quadratic polynomials 4x2 – 4x + 1 and verify the relationship between the zeros and the coefficients.
Answer» Let f(x) = 4x² ˗ 4x + 1 = (2x²) – 2(2x)(1) + (1)^2 = (2x – 1)² To find the zeroes, set f(x) = 0 (2x – 1)² = 0 x = 1/2 or x = 1/2 Again, Sum of zeroes = 1/2+1/2=1=1/1 = -b/a = (-Coefficient of x) / (Cofficient of x²) Product of zeroes = 1/2 x 1/2=1/4 = c/a = Constant term / Coefficient of x²

Find the zeros of the quadratic polynomials 4x2 – 4x + 1 and verify the relationship between the zeros and the coefficients.

Answer»

Let f(x) = 4x² ˗ 4x + 1

= (2x²) – 2(2x)(1) + (1)^2

= (2x – 1)²

To find the zeroes, set f(x) = 0

(2x – 1)² = 0

x = 1/2 or x = 1/2

Again,

Sum of zeroes = 1/2+1/2=1=1/1

= -b/a

= (-Coefficient of x) / (Cofficient of x²)

Product of zeroes = 1/2 x 1/2=1/4

= c/a

= Constant term / Coefficient of x²