Question

find the condition that 0 of polynomial p of x =ax² + bx + c are reciprocal of each other.

Answer 1

Given

A polynomial P(x) = ax² + bx + c

To Find

• The condition for which the roots are reciprocal to each other.

Concept

• The reciprocal of m is $\dfrac{1}{m}$

For a quadratic polynomial ax² + bx + c :-

• Sum of roots = $- \: \dfrac{b}{a}$

• Product of roots = $\dfrac{c}{a}$

If the roots are reciprocal,their products would be 1.

Hence, $\dfrac{c}{a}$ = 1

=> c = a.

Hence,the condition for which roots will be reciprocal is c = a.

Answer 2

$\huge\bold\red{Question}$

Find the condition that 0 of polynomial p of x =ax² + bx + c are reciprocal of each other.

$\huge\bold\green{Solution}$

$\sf{Given\: quadratic\: polynomial \:is \:P(x)}$$\sf{=ax^2+bx+c}$

$\sf{Given\: the\: roots\: are\: reciprocal\: to\: each\: other}$

$\sf{Let \:the\: roots\: b\: a,\frac{1}{a}}$

$\sf{Product \:of\: roots\: is \:a\times\frac{1}{a} =\frac{c}{a}}$

$\sf{\frac{c}{a}=1}$

$\sf{c=a}$

$\sf{Hence,\: the\: condition\: for \:which}$ $\sf{roots\:will\: be\: reciprocal \:is \:c = a}$