Question

find a quadratic polynomial the sum and product of whose zeros are zero minus root 2 respectively

Answer 1

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Answer 2

Concept Introduction:-

It might resemble a word or a number representation of the quantity's arithmetic value.

Given Information:-

We have been given that the sum and product of whose zeros are zero minus root $2$ respectively

To Find:-

We have to find that a quadratic polynomial the sum and product of whose zeros are zero minus root $2$ respectively

Solution:-

According to the problem

sum of zeros$=0$

$=-\sqrt{2}$

Let $\alpha$ and $\beta$ be the zeroes

sum of zeros$=0$

$\alpha +\beta =0$

product of zeros$=-\sqrt{2}$

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

∴ A quadratic equation

$x^2-(sum of zeros)x+(product of zeros)=0\\x^2-0+(-\sqrt{2})=0\\x^2-\sqrt{2}=0$

Final Answer:-

The correct answer is $x^2-\sqrt{2}=0$.

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