MCQ
A quadratic polynomial whose zeros are $5$ and $-3,$ is :
- A$ x^2+2 x-15 $
- B$ x^2-2 x+15 $
- ✓$ x^2-2 x-15 $
- DNone of these.
✓
Answer
Correct option: C.
$ x^2-2 x-15 $
Let $\alpha$ and $\beta$ be the zeros of the required quadratic polynomial.
Then, we have
$\alpha+\beta=5+(-3)=2$ and $\alpha\beta=5\times(-3)=-15$
Now, a quadratic polynomial whose zeros are $\alpha$ and $\beta$ is given by
$\text{p}(\text{x})=\text{x}^2-(\alpha+\beta)\text{x}+\alpha\beta$
$\Rightarrow\text{p}(\text{x})=\text{x}^2-(2)\text{x}+(-15)$
$=\text{x}^2-\text{2x}-15$
Then, we have
$\alpha+\beta=5+(-3)=2$ and $\alpha\beta=5\times(-3)=-15$
Now, a quadratic polynomial whose zeros are $\alpha$ and $\beta$ is given by
$\text{p}(\text{x})=\text{x}^2-(\alpha+\beta)\text{x}+\alpha\beta$
$\Rightarrow\text{p}(\text{x})=\text{x}^2-(2)\text{x}+(-15)$
$=\text{x}^2-\text{2x}-15$
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