1. 3x^2+7x-5=0 as roots α and β. Find a quadratic with roots 1/α + 1/β

2. 4x^2+7x-5=0 has the roots α and β. Find a quadratic with the roots α^2 + β^2

3. 2x^2+7x-3=0 as the roots α and β. Find a quadratic with the roots α+5/β and β+5/α.

4. x^2-6x-3=0 has the roots α and β . By substitution, find an equation with the roots 2α-1 and 2β-1.

5. x^3-3x^2+2=0 has the roots α ,β and γ. By substitution or otherwise, find a cubic with the roots 3α , 3β and 3γ.

6. x^4+ax^3+14x^2-18x+b=0 has the roots 3i, -3i, 1-3i and 1+3i. Find a and b.

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Roots of polynomials questions