Question

find the quadratic polynomial whose sum and product of zeroes are √2+1 and 1/√2+1 respectively

Answer 1

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Answer 2

The given question is we have to find the quadratic polynomial

The sum and product of zeroes the polynomial is given as

$\sqrt{2 } + 1 \\ \frac{1}{ \sqrt{2} + 1 }$

In algebra, the quadratic equation is any equation that can be rearranged in standard form as where x represents an unknown and the alphabets a, b, and c represent known numbers, where a is not equal to zero. if a is equal to zero, then the equation is linear, non quadratic and there is no square value

The general equation of the quadratic polynomial is

${x}^{2} - x(sum \: of \: zeroes) + product \: of \: zeroes$

The sum of zeroes and product of zeroes in the general term

$\alpha + \beta = \sqrt{2} + 1 \\ \alpha \beta = \frac{1}{ \sqrt{2} + 1}$

which is written in the format of alpha and beta is

${x}^{2} - x( \alpha + \beta ) + \alpha \beta = 0$

substituting the value in the above equation we get

${x}^{2} - x( \sqrt{2} + 1) + \frac{1}{ \sqrt{2} + 1}$

Thus the above expression is the final answer.

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