Quadratic Eqn theory WBJEE1975
Asked by baidshryans | 15th May, 2009, 04:09: PM
Let say that α and β are the roots of the equation ax2+bx+c=0.
Then, α + β = -b/a .....(1) and αβ = c/a.......(2)
From (1) & (2)
c/b = -αβ / α + β .............(3)
Now we have the relation between the coefficient of the polynomial as:
b3+a2c+ac2=3abc
⇒ b3 = 3abc - a2c - ac2
⇒ 1 = (3abc - a2c - ac2)/ b3
⇒ 1 = ac (3b -a - c) / b3
⇒ 1= (a/b)(c/b) (3-(a/b) - (c/b))
Sunstituting the values from equation (1), (2) and (3). The equation reduces to
(α+β)3 = αβ [3 (α+β) + αβ + 1]
Answered by | 16th May, 2009, 03:58: PM
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