Question

find the zeroes of the polynomial and find the relation between the zeroes and the coefficient.

4x^2-4x-1

Answer 1

Hi❤

$4 {x}^{2} - 4x - 1$

Solving the equation by 'Splitting the Middle Term method.'

$4 {x}^{2} - 2x - 2x - 1$

$2x(2x - 1) + 1(2x - 1)$

$(2x + 1)(2x - 1)$

So, its two zeroes are:

$x = \frac{ - 1}{2}$

And

$x = \frac{1}{2}$

Or,

$\alpha = \frac{ - 1}{2}$

$\beta = \frac{1}{2}$

We know that,

$\alpha + \beta = \frac{ - b}{a}$

$\alpha + \beta = \frac{4}{4} = 1$

Also,

$\alpha \beta = \frac{c}{a}$

$\alpha \beta = \frac{1}{4}$