Question

why x^2 - 3 = (x - √3) (x +√3)​

Answer 1

why x² - 3 = (x - √3) (x +√3)

Step by step explanation :

$\sf{ {x}^{2} - 3 = {x}^{2} - \sqrt{3} \times \sqrt{3} }$

$\sf{ {x}^{2} - 3 = {x}^{2} - {(\sqrt{3} )}^{1 + 1} }$

$\sf{ {x}^{2} - 3 = {x}^{2} - {(\sqrt{3} )}^{2} }$

• By Using identity, A²-B²=(A+B)(A-B)

$\sf{ {x}^{2} - 3 = (x + \sqrt{3} )(x - \sqrt{3}) }$

Zeros of the polynomial is √3 and -√3.

let Alpha be √3 and beta be -√3

Sum of zeros = alpha + beta = -b/a

√3-√3 = 0/3

0 = 0

Product of zeros = Alpha × beta = c/a

√3 × -√3 = -3 /1

-3 / -3