Question

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Answer 1

I think you use the idea that the roots must come in conjugate pairs if you do not want irrational coefficients

Answer 2

just find their respective conjugates as irrational roots always occur in conjugate pairs
for a+sqrt(b) the conjugate is of the form a- sqrt(b)

Answer 3

this is not going to be as hard as it looks

Answer 4

if the roots are \(7+\sqrt{3}\) and \(7-\sqrt{3}\) we can reconstruct the quadratic almost in your head
it will be
\[x^2-14x+49-3\] or
\[x^2-14x+46\]

Answer 5

ooh i see you just need the other roots! it is the conjugate of each one

Answer 6

the conjugate of \(a+\sqrt{b}\) is \(a-\sqrt{b}\)

Answer 7

pick those

Answer 8

lol first medal IN my Life YEAH ^-^