Question

$4x {}^{2} \: \: - \: 4x \: + \: 1$
Obtain the zeroes and verify relationship between zeroes and co efficient

Answer 1

♥️Hi there ♥️

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

So ,the value of 4x^2 -4x+1 is zero when 2x-1 =0 or x= 1/2

Zeroes are 1/2 ,1/2

$sum \: of \: the \: zeroes = \\ = \frac{1}{2} + \frac{1}{2} = 1 = ( \frac{ - 4}{4} ) = \frac{ - b}{a} = 1$
and

$product \: = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} = \frac{c}{a}$
Hence zeroes are equal to product and sum.

Thanks !!!

Hope it will helpful.