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Question

A quadratic polynomial, whose zeroes are $$-3$$ and $$4$$ is


A
x2x+12
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B
x2+x+12
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C
x22x26
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D
2x2+2x24
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Solution

The correct option is C $$\dfrac{x^2}{2} - \dfrac{x}{2} - 6$$
Quadratic equation with $$\alpha$$ and $$\beta$$ as roots can be written as
$$ x^2 - (\alpha + \beta) + \alpha\beta=0$$

Here, $$\alpha = -3$$ and $$\beta = 4$$
$$\therefore \alpha + \beta = -3 + 4 = 1$$
and $$\alpha - \beta = -3 \times 4 = -12$$

$$\therefore$$ The quadratic equation is
$$x^2 - (\alpha + \beta)x + \alpha\beta=0$$
$$\Rightarrow  x^2 - 1x - 12=0$$
$$\Rightarrow  \dfrac{x^2}{2} - \dfrac{x}{2} - \dfrac{12}{2}=0$$
$$\Rightarrow \dfrac{x^2}{2} - \dfrac{x}{2} - 6=0$$

Hence the quadratic polynomial is $$ \dfrac{x^2}{2} - \dfrac{x}{2} - 6$$

Mathematics

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