Question

find a quadratic polynomial,the sum and product of whoes zeros are the following numbers 1.
$- 3 < 2$
​

Answer 1

The given conditions if the zeroes are α and β is,

α+β = -3

αβ = 2

If α and β are the zeroes,

then the quadratic equation will be

(x-α)(x-β) = x² - x(α+β) + αβ

Hence the quadratic equation here would be

x² - x(-3) + (2) = x² +3x +2

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Answer 2

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sum of 2+√3 and 2-√3 is

$2 + \sqrt{3} + 2 - \sqrt{3} \\ = 4$

and product of 2+√3 and2-√3

$(2 + \sqrt{3} )(2 - \sqrt{3} ) \\ 2(2 - \sqrt{3} ) + \sqrt{3} (2 - \sqrt{3} ) \\ 4 - 2 \sqrt{3} + 2 \sqrt{3} - \sqrt{9} \\ 4 - 3 \\ 1$

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