Question

find a quadratic polynomial whose zeroes are reciprocal of zeroes of the polynomial. f(x) = ax^2+bx+c, a and c is not equal to zero

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Answer 1

Answer:

(x+1)^2 could be the answer of your question.

Step-by-step explanation:

I'm not quite sure about your question what you meant.

But I think this could be your answer.

According to the question, we have to find a quadratic polynomial whose zeroes are the reciprocal of zeroes of that very polynomial.

Look for instance, only 1 is the number whose reciprocal remains the same.

so,

  f(x) = x^2+2x+1

       =(x+1)^2

       =(x+1)(x+1)

 Now,

          (x+1)(x+1) = 0

           x+1 = 0     0r,    x+1 = 0

            x = -1        or,   x = -1

       look the reciprocal of -1 is 1/-1 which means -1.

So this could be your answer.

You can also use this formula (x-1)^2.