Question

find the quadratic polynomial whose zeroes are √3+√5 and √5 - √3​

Answer 1

hey mate here is ur answer =

Sum of roots= root 3+root 5+root 5-root 3

=2root 5.

product of roots=(root 5)^2-(root3)^2=2.

quadratic equation =

x^2-(sum of roots)x+(product of roots)

=x^2-(2root5)x+2.

hope it helps .

☆☆☆

Answer 2

$\huge \mathfrak \red{answer}$

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Question:

find the quadratic polynomial whose zeroes are √3+√5 and √5 - √3

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step to step explanation

⇒Given quadratic polynomial whose zeroes are √3+√5 and √5 - √3

$\sf{ \:now \: Let \: α = (3+ \sqrt{5} ) β \: = (3- \sqrt{5)}}$

Now we used the formula of polynomial

$⇒ \bf{ \: { \boxed{ \green{ \tt{qudratic \: polynomial = {x}^{2} - (sum \: of \: zeroes)x + product \: of \: zeroes \: }}}}}$

⇒Now sum of zeroes

$⇒ \rm{ \alpha + \beta }$

$\rm{(3+ \sqrt{5} ) + (3- \sqrt{5})}$

$\rm{6}$

$\bf{ { \boxed{ \green{ \tt{ \alpha + \beta = 6 \: }}}}}$

⇒now Product of zeroes

$⇒ \tt{ \alpha \beta }$

$\tt{(3+ \sqrt{5} ) (3- \sqrt{5} )}$

$\tt{ {3}^{2} - ( \sqrt{5) }^{2} }$

$\tt{9 - 5}$

$\tt{4}$

$\bf{ \: { \boxed{ \green{ \tt{ \alpha \beta = 4 \: }}}}}$

then qudratic polynomial is

$\rm \red{ {x}^{2} - 6x + 4}$

x² - (α + β)x + αβ

I hope it's help uh

mark it as brainlist