The correct option is
D None of these
Let p(x) has three distinct roots x1,x2,x3
As x1,x2 are roots of p(x), we can
write p(x) as:
p(x)=(x−x1)(x−x2)g(x)
Since p(x) has degree 2,g(x) must be
a constant k.
Further, we have p(x3)=0
⇒k(x3−x1)(x3−x2)=0
Since we assumed x1,x2,x3 to be
distinct (If any two would be same,
roots won't be 3 anymore), k must be
equal to zero. Hence, p(x) is zero
for any value of x. Hence, the only
possibility for this to happen is if
a=b=c=0.
No Option matches correctly.
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