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if alpha beta gamma are the roots of the equation 2 x cube + x square + X + 1 is equal to zero then find the value of summation 1 by Alpha square |
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Answer» Answer: A − 4 15
3 −3x 2 +6x+1=0, Sum of ROOTS: α+β+γ= 2 3
, Product of roots: αβγ= 2 −1
, Sum of roots taken 2 at a time: Σαβ= 2 6
=3 Now, we know that (α+β+γ) 2 =α 2 +β 2 +γ 2 +2(αβ+βγ+γα) Re-arranging, we get α 2 +β 2 +γ 2 =(α+β+γ) 2 −2(Σαβ) α 2 +β 2 +γ 2 =( 2 3
) 2 −2×3= 4 9
−6=− 4 15
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