Question

find a quadratic polynomial each with the given numbers as the sum and products of its zeros are 2√3-1,3-√3​

Answer 1

♠️Question:

Find a quadratic polynomial each with the given numbers as the sum and products of its zeros are 2√3-1,3-√3.?

♠️Answer:

Let there be a Quadratic polynomial p(x)

$\large{ \sf{ \alpha \: and \: \beta \: are \: zeroes \: of \: p(x)}}$

Then,

$\large{ \sf{ \boxed{ \red{p(x) = {x}^{2} - ( \alpha + \beta )x + \alpha \beta }}}}$

Here sum of zeroes= 2root3 -1

And product of zeroes = 3- root3

That means,

$\large{ \sf{ \to \: given \: \: \alpha + \beta = 2 \sqrt{3} - 1}} \\ \large{ \sf{ \to \: and \: \alpha \beta = 3 - \sqrt{3} }}$

Then the required polynomial p(x) is

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

♠️So final answer:

$\large{ \boxed{ \bold{ \red{ {x}^{2} - (2 \sqrt{3} - 1)x + 3 - \sqrt{3} }}}}$

Answer 2

Step-by-step explanation:

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