Question
Find a quadratic polynomial whose zeros are 2 and -5.
✓
Answer
It is given that the two roots of the polynomial are 2 and -5.
Let $\alpha=2$ and $\beta=-5$
Now, sum of the zeroes, $\alpha+\beta=2+(-5)=-3$
Product of the zeroes, $\alpha\beta=2\times-5=-10$
$\therefore$ Required polynomial $\text{x}^2-(\alpha+\beta)\text{x}+\alpha\beta$
$=\text{x}^2-(-3)\text{x}+(-10)$
$=\text{x}^2+\text{3x}-10$
Let $\alpha=2$ and $\beta=-5$
Now, sum of the zeroes, $\alpha+\beta=2+(-5)=-3$
Product of the zeroes, $\alpha\beta=2\times-5=-10$
$\therefore$ Required polynomial $\text{x}^2-(\alpha+\beta)\text{x}+\alpha\beta$
$=\text{x}^2-(-3)\text{x}+(-10)$
$=\text{x}^2+\text{3x}-10$
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