# ROOTS AND COEFFICIENTS OF QUADRATIC EQUATION WORKSHEET

(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)

(iv)  [(α + 3)/β] + [(β + 3)/α]

(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)           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

(iii) α2β and β2α

(4)  If α, β are the roots of 7x2+ax+2=0 and if β − α = −13/ 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.

(6)  If one root of the equation 3x2 + kx + 81 = 0 (having real roots) is the square of the other then find k.

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