Question

Find the condition in which one of the zeros of the polynomial ax^2+bx+c is negative reciprocal of other

Answer 1

Given that the polynomial,p(x) = ax²+bx +c has zeros which are reciprocal to each other

If one of zero of the polynomial is @,then the other would be 1/@

We know that,

Product of Zeros: constant term/x² coefficient

Here,

(@).(-1/@) = c/a

→-1 = c/a

→-a = c

If a and c are equal,the polynomial would have zeros which are reciprocal and negative to each other

Answer 2

Answer: (c + a = 0)

Step-by-step explanation:

Given polynomial

P(x) = ax² + bx + c

Let the roots of the this equation be α and -1/α

We know that,

Product of roots = c/a

α × (-1/α) = c/a

-1 = c/a

-a = c

c + a = 0

This is the required condition for which one of the zeros  of the given polynomial is negative reciprocal of other.