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Coefficients of a Polynomial

Find the quad...

Question

Find the quadratic polynomial where sum and product of the zeros are $a$ and $\frac{1}{a}$ .

a x^{2} + a^{2} x + 1 = 0

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a x^{2} - a x + 1 = 0

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a x^{2} - a^{2} x - 1 = 0

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a x^{2} - a^{2} x + 1 = 0

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Solution

The correct option is B $a x^{2} - a^{2} x + 1 = 0$
$∴ x^{2} + (- a) x + \frac{1}{a} = 0$
$a x^{2} - a^{2} x + 1 = 0$

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