1. Write each of the following expression in terms of α + β and αβ .
(iii) (3α - 1)(3β -1)
2. The roots of the equation 2x2 − 7x + 5 = 0 are α and β. Without solving for the roots, find
3. The roots of the equation x2 + 6x − 4 = 0 are α, β. Find the quadratic equation whose roots are
(i) α 2 and β 2
(ii) 2/α and 2/β
(iii) α2β and β2α
4. If α, β are the roots of 7x2 + ax + 2 = 0 and if β − α = -13/7. Find the values of a.
5. If one root of the equation 2y2 − ay + 64 = 0 is twice the other then find the values of a.
6. If one root of the equation 3x2 + kx + 81 = 0 (having real roots) is the square of the other then find k.