Question

Write a quadratic polynomial, sum of whose zeros is $2\sqrt{3}$ and their product is 2.

Answer 1

SOLUTION :

Let α  and β are the zeroes of the quadratic polynomial

Given :  α +  β = 2√3  …………….(1)

αβ = 2 ……………..(2)

Then, the quadratic polynomial is :  

k[x² –(sum of the zeroes)x + (product of the zeroes)]

k[x² –(α + β)x + (α β)]

=k[ x² - (2√3) x + (2)]

[From eq 1 & 2]

= k[ x² - 2√3x - 2]

[K is any non zero real number]

Hence, the quadratic polynomial is f(x) =k[ x² - 2√3x - 2]

HOPE THIS ANSWER WILL HELP YOU..

Answer 2

$\color{red}\huge\mathfrak{hello \: friend!!}$

$<b>sum of zeroes=2√3 product of zeroes=2</b>$

$polynomial = k( {x}^{2} - (sum)x + product \\ k( {x}^{2} - 2 \sqrt{3} + 2)$

$<marquee> ✌️❣️hope it helps u mark it brainliest❣️✌️</marquee>$