Find a quadratic polynomial with the given numbers as the sum and product of zeroes respectively: $1,\ 1$.

Given: The sum and the product of the zeroes of a quadratic polynomial are respectively: $1,\ 1$.

To do: To find the quadratic polynomial.

Solution:

Let $\alpha$ and $\beta$ are the zeroes of the polynomial.

As given, 

Sum of the zeroes$=\alpha +\beta=1$

Product of the zeroes$=\alpha.\beta=1$

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

$\Rightarrow x^{2}-1.x+1=0$

$\Rightarrow x^{2}-x+1=0$

Thus, the required quadratic polynomial is $x^2-x+1$.

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Updated on: 10-Oct-2022

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