If alpha and beta are roots of the equation x^2 +mx +n=0, find the roots of nx^2+(2n-m^2)x+n=0 in terms of alpha and beta.

[darn this is probably real simple but i havent got the hang of how to do these ones]

ok here are a few more that i ended up not being able to do...

18. If the roots of the equation x^3+px^2+qx+r=0 form consecutive terms of a gemetric sequence, prove that q^3=p^3r.

Show that this condition is satisfied for the equation 8x^3-100x^2+250x-125=0 and solve this equation.

22.If alpha, beta, delta are the roots of 3x^3+8x^2-1=0 find the value of

(beta +1/delta)(delta +1/alpha)(alpha +1/beta)

i did this question but ive continuously gotten 2/3.. can someone tell me what ive done wrong? because the answer was -6.

[darn this is probably real simple but i havent got the hang of how to do these ones]

ok here are a few more that i ended up not being able to do...

18. If the roots of the equation x^3+px^2+qx+r=0 form consecutive terms of a gemetric sequence, prove that q^3=p^3r.

Show that this condition is satisfied for the equation 8x^3-100x^2+250x-125=0 and solve this equation.

22.If alpha, beta, delta are the roots of 3x^3+8x^2-1=0 find the value of

(beta +1/delta)(delta +1/alpha)(alpha +1/beta)

i did this question but ive continuously gotten 2/3.. can someone tell me what ive done wrong? because the answer was -6.

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