Question

Find the condition that zeroes of a polynomial p(x)=ax2

+bx+c are reciprocal

of each other.​

Answer 1

Step-by-step explanation:

zeroes are reciprocal so c= 1(alpha*beta)

many polynomials can satisfy this condition

for example

p(x)= x^2+2x+1

where a=1

b=2

c=1

and zeroes are 1,1 (1 is reciprocal of 1 itself)

please mark BRAINIEST

Answer 2

$\tt SoluTion$

Let, zeroes of ax²+bx+c are

x and 1/x (reciprocal of each other )

then,

sum of zeroes should be = -b/ a

$\tt \frac{1}{x}+x=\frac{-b}{a}\\\\\boxed{\tt \frac{1+x^2}{x}=\frac{-b}{a}}$

and

product of zeroes = c / a

$\tt \frac{1}{x}*x=\frac{c}{a}\\\\{\tt 1 = \frac{c}{a}}$

i.e,

$\boxed{\tt c=a}$