Find the quadratic polynomial whose zeros are reciprocal of the zeros of the polynomial f(x) :- ax^2+bx+c, where a is not equal to zero, c is not equal to zero. Then find the polynomial?

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Answer 1 · 2018-04-12T17:44:03

# cx^2+bx+a, a!=0, c!=0#.

Let #p and q# be the zeroes of the quadr. poly. #ax^2+bx+c#,

#(a!=0, c!=0)#.

Then, we have, #p+q=-b/a, and, pq=c/a......(square)#.

Let #P and Q# be the zeroes of the reqd. quadr. poly.

Then, by what is given, #P=1/p, and Q=1/q#.

Utilising #(square)#, then,

# P+Q=1/p+1/q=(q+p)/(pq)=(-b/a)/(c/a)=-b/c, and, #

#PQ=1/p*1/q=1/(pq)=a/c#.

Therefore, the reqd. quadr. poly. is given by,

#x^2-(P+Q)x+PQ=x^2+b/c*x+a/c# or, what is the same as

to say, #cx^2+bx+a, a!=0, c!=0#.

Find the quadratic polynomial whose zeros are reciprocal of the zeros of the polynomial f(x) :- a*x^2+b*x+c, where a is not equal to zero, c is not equal to zero. Then find the polynomial?