Question

Find the quadratic polynomial whose zeros are the reciprocal of the zero of 4 x²-3 x -1

Answer 1

Answer:

p(x)=4x²-3x-1

=4x²-4x+x-1

=4x(x-1)+1(x-1)

=(4x+1)(x-1)

x=-¼. x=1

zeroes are -¼ and 1

Their reciprocals -4 and 1

Sum of the Zeroes =-4+1=-3

Product of the Zeroes=-4×1=-4

A quadratic polynomial is

x²+3x-4=0