Question

if alpha and beta are the zeroes of x^2-2x-1, form a quadratic polynomial whose zeroes are 2alpha+1 and 2beta-1​

Answer 1

Answer:

Step-by-step explanation:

DEAR HUMAN BEING ,

= P(x) = x^2 - 2x - 1

by quadratic formula ,

x = 1 + root 2 and ,  x = 1 - root 2 ,

= alpha = 1 + root 2 and , beta = 1 - root 2

the other polynomial that we have to find has zeroes 2alpha+1 and 2beta-1 ,

= SUM OF ZEROES = 2 ALPHA + 1 + 2 BETA - 1 = 2(1 + ROOT 2 + 1 - ROOT 2)

= 2 * 2 = 4

= PRODUCT OF ZEROES = (2 ALPHA + 1 ) (2 BETA - 1 )

= 4 * ALPHA * BETA - 2 ALPHA + 2 BETA - 1

= -4 - 1 - 2(1 + ROOT 2) + 2( 1 - ROOT 2)

= -14 ROOT 2

NOW , THE REQUIRED POLYNOMIAL IS

F(x) = k( x^2 - ( SUM OF ZEROES ) + ( PRODUCT OF ZEROES )

      = K( X^2 - 4x + 14 ROOT 2).

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Answer 2

Answer:

Ok

Step-by-step explanation:

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