Question

If alpha and beta are zeros of the polynomial x square - 2 x minus one ,form a quadratic polynomial whose zeros are 2 alpha minus ,2 beta minus one
...pls someone solve this ..urgent..thanks

Answer 1

Let Alpha and beta are the zero of the polynomial X²-2X-8.

P(X) = X²-2X-8

Here,

A = 1 , B = -2 and C = -8

Sum of zeroes = -B/A

Alpha + Beta = -(-2)/1

Alpha + Beta = 2/1

Alpha + Beta = 2

And,

product and zeroes = C/A

Alpha × Beta = -8/1

Alpha × Beta = -8

Sum of zeroes of the Quadratic polynomial whose zeroes are 2alpha and 2 beta .

Sum of zeroes = (2alpha + 2beta) = 2(Alpha + Beta) = 2(2) = 4

And,

Product of zeroes = 2Alpna × 2beta = 4( Alpha × Beta)= 4(-8) = -32

Therefore,

Required Quadratic polynomial = X²-(sum of zeroes)X + Product of zeroes

=> X²-(4)X + (-32)

=> X²-4X -32

Answer 2

check the attachment