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Question

If $$\alpha,\ \beta,\ \gamma,\delta$$ are the roots of the equation $$x^{4}-16x^{3}+86x^{2}-176x+105=0$$, then match the elements of List I with elements of List II:
List IList II
I) $$\sum \alpha$$a) $$86$$
II) $$\sum \alpha \beta$$b) $$105$$
III) $$\sum \alpha \beta \gamma$$c) $$16$$
IV) $$\alpha \beta \gamma \delta$$d) $$176$$

Correct order for I, II, III, IV is:


A
c, a, b, d
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B
c, b, a, d
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C
c, b, d, a
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D
c, a, d, b
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Solution

The correct option is D c, a, d, b
Using theory of equation,
$$\sum \alpha=-\cfrac{b}{a} = 16$$
$$\sum \alpha \beta=\cfrac{c}{a} =86$$
$$\sum \alpha \beta \gamma=-\cfrac{d}{a}=176$$
$$\alpha \beta \gamma \delta=\cfrac{e}{a}=105$$

Mathematics

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