[[1]] is the condition that the zeroes of the polynomial p(x)=ax2+bx+c are reciprocal of each other.

c = a is the condition that the zeroes of the polynomial p(x)=ax2+bx+c are reciprocal of each other.
Let one of the roots of the quadratic equation

p (x) = a x^{2} + bx + c

m

then, according to the question, the second root of the polynomial will be

\frac{1}{m}

as the reciprocal of the first one.
The product of the roots of the quadratic equation is the ratio of the coefficient of

x^{0} and x^{2} .

Here, the coefficient of

x^{2}

is a while the coefficient of x0 is c.
Hence,

m \times \frac{1}{m} = \frac{c}{a}

1 = \frac{c}{a}

c = a
Hence,

c = a

is one of the conditions that the zeroes of the polynomial

p (x) = a x^{2} + bx + c

are reciprocal of each other.

JEE