If $\alpha$ and $\beta$ are the zeroes of a polynomial such that $\alpha+\beta=-6$ and $\alpha\beta=5$, then find the polynomial.
Given: $\alpha$ and $\beta$ are the zeroes of a polynomial such that $\alpha+\beta=-6$ and $\alpha\beta=5$.
To do: To find the polynomial.
Solution:
The polynomial is:
$p( x)=x^2-( sum\ of\ the\ zeroes)x+( product\ of\ the\ zeroes)$
$p( x)=x^2-( \alpha+\beta)x+\alpha\beta$
$p( x)=x^2-( -6)x+( 5)$
$p( x)=x^2+6x+5$
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