Question

find the condition that zeros of polynomial p(x)=ax2+bx+c are reciprocal of each other​

Answer 1

Let m be its one zero then another zero will be 1/m.

Now ,

Product of zeros = c/a

→m×1/m = c/a .

→1=c/a

→a = c .

Thus the required condition for the zero is c=a .

Answer 2

Answer:

Step-by-step explanation:

Given:

$ax^{2} +bx+c$ has zeroes that are reciprocal of each other.

To find:

Condition to satisfy it.

Solution:

Let zeroes be $y and 1/y$

$ax^{2} +bx+c$=0

$Product of zeroes = constant/Product of x^2$

==>$y *1/y=c/a$

$1=c/a\\a*1=c\\a=c$

Hence, the condition for which polynomial has zeroes reciprocal of each other is $a=c$

Hope it helps....