Find a quadratic polynomial with the given numbers as the sum and product of zeroes respectively: $4,\ 1$
Given: The sum and product of zeroes respectively are : $4,\ 1$
To do: To find the quadratic polynomial.
Solution:
Let $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial.
As given, sum of the zeroes$=\alpha+\beta=4$
Product of the zeroes$=\alpha\beta=1$
The quadratic polynomial is:
$x^{2}-( \alpha +\beta )+\alpha \beta=0$
$x^{2}-4x+1=0$
The required quadratic polynomial is $x^2-4x+1$
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