If , and are the roots of the equation x^3-8x+8=0, then ^2 and 1 αβ are respectively

Question

Accepted Answer

Correct answer: D. (d) Given equation x^3-8x+8=0 ∴ =0 , αβ=-8 , αβγ=-8 ⇒ ( + + )^2= ^2+ ^2+ ^2+2 ( αβ+ βγ+ γα ) ⇒0= ^2+ ^2+ ^2+2 (-8 ) ⇒ ^2=16. Now _2 1 αβ+ 1 βγ+ 1 αγ= αβγ ( + + ) ^2 ^2 ^2= + + αβγ=0 ∴ ^2=16 , 1 αβ=0.

$If α, β and γ are the roots of the equation x^{3} - 8 x + 8 = 0, then \sum α^{2} and \sum \frac{1}{αβ} are respectively$

Solution

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