Question

Find the condition that zeroes of the polynomial ax² + bx + c are reciprocal of each other

Answer 1

For the quadratic equation ax^2 + bx + c
if α and β are the roots of this equation, then :

α+β=-b/a and
αβ=c/a

reciprocal of each other that is α= 1/ β

αβ=c/a
1/β *β =c/a
c/a=1
c=a