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Relations between Roots and Coefficients : Higher Order Equations

α ,β are the ...

Question

$α, β$ are the roots of $a x^{2} + b x + c = 0$
$L_{1} = L t x \to α \frac{1 - c o s ({a x}^{2} + b x + c)}{{(x - α)}^{2}}$
$L_{2} = L t x \to β \frac{1 - c o s ({a x}^{2} + b x + c)}{{(x - β)}^{2}}$
$L_{3} = L t (x - α) (x - β) \to 0 \frac{1 - c o s ({a x}^{2} + b x + c)}{{(x - α)}^{2} {(x - β)}^{2}}$

A

L_{1} = L_{2}

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B

L_{1} = L_{3} {(α - β)}^{2}

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C

L_{2} = L_{3} {(α - β)}^{2}

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D

L_{3} = \frac{a^{2}}{2}

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Solution

The correct options are
A $L_{1} = L_{2}$
B $L_{1} = L_{3} {(α - β)}^{2}$
C $L_{2} = L_{3} {(α - β)}^{2}$
D $L_{3} = \frac{a^{2}}{2}$

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