Question

find the polynomail whose zeroes are √2 and -√2

Please answer with explanation.​

Answer 1

Your polynomial is:-

(x^2-2).

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Answer 2

$\alpha=\sqrt{2}\\ \beta=-\sqrt{2}$

Sum of zeroes = √2 - √2 = 0

Product of zeroes = √2 × -√2 = -2

Quadratic equation = x² - (Sum of zeroes) x + (Product of zeroes)

$=x^2-(0)x+(-2)\\=x^2-2$

Hence the polynomial is :

⇒ x² - 2