Quadratic Eqn theory WBJEE1975

Asked by baidshryans | 15th May, 2009, 04:09: PM

Expert Answer:

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

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.