Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

4x² – 4x + 1

To find the zeros of the polynomial let us first solve the polynomial by equating it to zero. Factorizing the given polynomial

4x² – 4x + 1 = 0

To factorize the polynomial we have,

Sum of the value should be equal = -4

Product should be equal to = 4 × 1

= 4

So two numbers are -2, -2

4x² – 2x – 2x + 1 = 0

2x(2x – 1) – 1(2x – 1) = 0

(2x-1)(2x-1) = 0

2x-1 = 0 or 2x-1 = 0

Both the parts are same.

Solving them,

2x-1 = 0

2x = 1

x = 1/2

When we compare the above quadratic equation with the generalized one we get,

ax² + bx + c = 0

∴ a = 4, b = -4, c = 1

Sum of zeroes = -b / a

= - (-4) / 4

= 1

Product of zeroes = c / a

= 1 / 4

= 1/4