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1. the equation x^2+6x+10=0 has roots a and b

find the quadratic equation with interger coeffiecients with roots a^3b and ab^3

im stuck!! thanks alot
2. (Original post by sarah12345)
the equation x^2+6x+10=0 has roots a and b
no it doesnt have any roots, real roots anyway. possibly too hard for me
3. (Original post by sarah12345)
the equation x^2+6x+10=0 has roots a and b

find the quadratic equation with interger coeffiecients with roots a^3b and ab^3
a + b = - 6

ab = 10

a^3 b + a b^3 = ab (a^2 + b^2) = ab ((a+b)^2 - 2ab) = (10)(36-20) = 160

(a^3 b) (a b^3) = (ab)^4 = 10000

x^2 - 160x + 10000
4. (Original post by RichE)
a + b = - 6

ab = 10

a^3 b + a b^3 = ab (a^2 + b^2) = ab ((a+b)^2 - 2ab) = (10)(36-20) = 160

(a^3 b) (a b^3) = (ab)^4 = 10000

x^2 - 160x + 10000
thanks

do u know how you could do it by writting the roots in terms of another variable?
5. (Original post by sarah12345)
do u know how you could do it by writting the roots in terms of another variable?
not sure what you mean - can you expand on this?
6. well the way i tried to do it is to say that u=a^3b
the rearange it to get u in terms of one of the roots and sub this into the equation but i got the wrong answer
does that make any sence?
7. (Original post by sarah12345)
well the way i tried to do it is to say that u=a^3b
the rearange it to get u in terms of one of the roots and sub this into the equation but i got the wrong answer
does that make any sence?
you already have "u in terms of the roots"

these questions are always the same and amount to writing symmetric expressions in a and b, in terms of the elementary symmetric polynomials a+b and ab
8. its how it says to do it in the book but your way works so ill leave it

thanks alot

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