Find the quadratic polynomial whose zeroes are $-2$ and $-5$.
Given: Zeroes of the quadratic polynomial are $-2$ and $-5$.
To do: To find the polynomial.
Solution:
As given, zeroes of the quadratic polynomial are $-2$ and $-5$.
Therefore, Sum of the zeroes $\alpha+\beta=-2+( -5)=-7$
Product of the zeroes $\alpha\beta=( -2)\times ( -5)=10$
Thus, the polynomial is : $x^2-( \alpha+\beta)x+\alpha\beta=0$
$\Rightarrow x^2-( -7)x+10=0$
$\Rightarrow x^2+7x+10=0$
Therefore, the polynomial is $x^2+7x+10=0$.
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