Question

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

Answer 1

Here let the zeros be

$\alpha \:and \beta$

Alpha + beta = -b/a

Alpha × beta = c/a .

Now reciprocal of zeros ,

1/alpha + 1/beta = (alpha + beta)/alpha ×beta = (-b/a)/(c/a)= -b/c .

Similarly ,

1/alpha × 1/beta = 1/(c/a)=a/c .

Thus , the required polynomial is x^2 -( -b/c)x +a/c or ,

= cx^2 +b/c +a

Answer 2

Answer:

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

Given the roots are reciprocal to each other

Let the roots be ∝, 1/∝

⇒ Product of roots is ∝ * 1/∝ = c/a

⇒ c/a = 1

⇒ C = a

HOPE THIS HELPS YOU!!!