(1) Write each of the following expression in terms of α + β and α β
(i) (α / 3β) + (β / 3α) Solution
(ii) (1 / α2β) + (1 / β2α) Solution
(iii) (3α - 1) (3β - 1) Solution
(iv) [(α + 3)/β] + [(β + 3)/α] Solution
(2) The roots of the equation 2x2 −7x + 5 = 0 are α and β. Without solving for the roots, find
(i) (1/α) + (1/β) Solution
(ii) (α/β) + (β/α) Solution
(iii) [(α + 2)/(β + 2)] + [(β + 2)/(α + 2)] Solution
(3) The roots of the equation x2 + 6x − 4 = 0 are α, β. Find the quadratic equation whose roots are
(i) α2 and β2 Solution
(ii) 2/α and 2/β Solution
(iii) α2β and β2α Solution
(4) If α, β are the roots of 7x2+ax+2=0 and if β − α = −13/7 Find the values of a. Solution
(5) If one root of the equation 2y2 − ay + 64 = 0 is twice the other then find the values of a. Solution
(6) If one root of the equation 3x2 + kx + 81 = 0 (having real roots) is the square of the other then find k. Solution
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