If roots of ax2 + x +b = 0 be real and unequal, show that roots of x2 +1/x = 4√ab be imaginary
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Answer:
The roots are complex conjugate
Explanation:
If the roots of
ax2+2bx+c=0
are real and distint then b2−ac>0
Now grouping
(a+c)(ax2+2bx+c)−2(ac−b2)(x2+1)=0
we have
(a2+2b2−ac)x2+2b(a+c)x+2b2+c(c−a)=0
and solving for x
x=−b(a+c)+√(4b2+(a−c)2)(ac−b2)a2+2b2−ac
and ac−b2<0 so the roots are complex conjugate
I hope this will help u........plz mark it as a brilliant ans
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