Question

50 Points :v:

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If a cubing equation $x^3 - x^2 + 2x + 3$= 0

Has roots α, β, γ.

Then give the new equation for which the roots are as ;

1) α + β, β + γ, γ + α
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Answer 1

Answer:

equation : x^3-x^2+2x+3 = 0

zeroes : a,b and y ( a= alpha , b = beta , c = gamma )

• sum of zeroes = a+b+y = -b/a .......(1)

= 1/1

• ab + by + ya = c/a = 2......(2)
• product = aby = d/a = 3/1

zeroes of new polynomial : a+b , b+y , y+a

• sum of zeroes = a+b+b+y + y +a.

= 2( a+b+y )

from (1),

a+b+y = 1

2(a+b +y ) = 2 = -B/A

• (a+b)(b+y ) + (b+y)(y+a) + (y+a)(a+b)
• = ab +ay + b^2+by + by+ab + y^2+ay + ya +by + a^2 + ab
• = 3ab + 3ay + 3by + a^2 + b^2 + y^2
• = 3(ab + ay + by ) + a^2 + b^2 + y ^2

from (2),

===> 6 +a^2 + b^2 + y^2 = c/a

Answer 2

Answer:

see the attachment for answer

Step-by-step explanation:

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