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 III) $$\sum \alpha$$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
B
c, b, a, d
C
c, b, d, a
D
c, a, d, b

Solution

The correct option is D c, a, d, bUsing 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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