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Q.

If α and β,α and γ,α and δ are the roots of the equations ax2+2bx+c=0,2bx2+cx+a=0 and cx2+ax+2b=0 respectively, where e, b, and c are positive real numbers, then α+α2=

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a

abc

b

a + 2b + c

c

-1

d

0

answer is C.

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Detailed Solution

Since α is root of all equationsaα2+2bα+c=02bα2+cα+a=0cα2+aα+2b=0Adding we get (a+2b+c)α2+α+1=0a+2b+c≠0 as a,b,c>0⇒α2+α+1=0 or α2+α=−1
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