exam Maths Puzzle Numerical Ability

Rationalize the denominator:

sqrt 2 minus 4 over z^2 plus 2 over z^4

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exam Other Question

Polynomial ax^3+ bx^2+cx+d has integral coefficients a,b,c,d. ad is odd and bc is even.
PROVE THAT at least 1 root of the polynomial is irrational

I used sum of roots and produ help verifying the identity

sin^2(theta/2)=csc(theta)-cot(theta)/2csc theta