Question

find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficient 4 x square - 4 x + 1 ​

Answer 1

P(x)

$4x {}^{2} - 4x + 1 = 0 \\ 4x {}^{2} - 2x - 2x + 1 = 0 \\ 2x(2x - 1) - 1(2x - 1) = 0 \\ (2x - 1)(2x - 1) = 0 \\ x = 1 \div 2 \: or1 \div 2$

Now, verifying the relationship between zeros and coefficients

$\alpha + \beta = - b \div a$

so, 1/2+1/2 = 4/4

2/2 = 1

1 = 1

verified (1)

now,

$\alpha \times \beta = c \div a$

1/2 × 1/2 = 1/4

1/4=1/4

Verified (2)

Hope it helps you!!!