Question

If alpha and beta are the zeroes of the polynomial x^2+8x+6.Form a polynomial whose zeroes are 1/alpha^2 and 1 /beta^2​

Answer 1

Answer:

Let p(x)= x²+8x+6

since à and ß are the zeroes of given polynomial

à+ß=-b/a

à+ß= -8/1= -8

à.ß=c/a

à.ß=6/1=6

required quadratic polynomial whose zeroes are

1/ಠand 1/߲ is

=k[x²-(sum of zeros) x+product of zeros]

where k is a constant term

=k[x²-(1/à²+1/ß²)x+1/à²×1/ß²]

=k[x²-(à²+ß²/à².ß²)+1/à².ß²]

=k[x²-{(à+ß)²-2à.ß/(à.ß)²}x+1/(à.ß)²]

=k[x²-{(-8)²-2×6/6²}x+1/6²]

=k[x²-{64-12/36)x+1/36]

=k[x²-52x/36+1/36]

=k[x²-13x/9+1/36]

taking k=36

=36[x²-13x/9+1/36]

=36x²-52x+1

Answer 2

Answer:

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