Let a, b, c be non-zero real roots of the equ | vedclass

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Question

(c)

We have,

$a b c =-c$

$a b+b c+c a =b$

$And\,\,a+b+c =-a 	ext { From Eq. (i), }$

$a b =-1(	ext { since } c 
eq 0 	ext { ) }$

Vedclass · Accepted Answer

There are exactly two such triples a, $b, c$

Vedclass · Answer

(c)

We have,

$a b c =-c$

$a b+b c+c a =b$

$And\,\,a+b+c =-a 	ext { From Eq. (i), }$

$a b =-1(	ext { since } c 
eq 0 	ext { ) }$

So, from Eq. $(iii)$, $c=-2 a+\frac{1}{a}$

and from Eq. $(ii)$ we get,

$\quad-1+2-\frac{1}{a^2}-2 a^2+1=-\frac{1}{2}$

$\Rightarrow \quad \quad 2 a^4-2 a^2-a+1=0$

$\Rightarrow \quad(a-1)\left(2 a^3+2 a^2-1ight)=0$

$	ext { From here we get only two real and }$

$	ext { non-zero values of } a, 	ext { hence there exists }$

$	ext { two triplets of }(a, b, c)$

Let $a, b, c$ be non-zero real roots of the equation $x^3+a x^2+b x+c=0$. Then,

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