Question

quadratic equation.......

Answer 1

Heya!
--------

=====================================================
♦Quadratic Equation ♦
=====================================================

⭐Given that =>
==============


♦2 is a root of the Equation !


$= > let \: \alpha \: and \: \beta \: be \: the \: two \: roots$
We know that ,

$\alpha + \beta = 0(given) \\ \\ \alpha = 2 \\ \\ = > 2 + \beta = 0 \\ \\ = > \beta = - 2$
♦Now Sum of Roots = 0

♦Product of Roots = -4


⭐p (x) = x² -sx + p.............(1)


Put Values in (1)


P (x ) = x² - 0x - 4

=>> P ( x ) = x² - 4 =0
================


✔Option (b) is correct ✔


=======================================================

Answer 2

given sum of roots (x+ y) = 0

let ,one root ,y = 2

sum of roots = x + y =0

x + 2 = 0

x = - 2 ,

product of roots ,

xy = -2 × 2= - 4

so the obtained quadratic polynomial

= X^2 - ( x + y ) X + xy

= X^2 - ( 0) X - 4

= X^2 - 4 = 0

hence, option (b) is the right answer.

●hope it helps ●