Question

100 points....
IIT

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maths please help

Answer 1

hello...


please refer the above. attachment.. ..


thank you

Answer 2

Hello user☺☺

For an equation to have equal roots it's discriminant must be equal to 0

So, here the second equation us given as ..

x^3 - px^2 + qx = 0

x (x^2 - px + q ) = 0

(x^2 - px + q ) = 0 and x = 0

So, one root of the cubic equation is 0

Calculating the discriminant , we get....

D = 0 (for equal roots)

p^2 - 4q = 0 .... (1)

Let us assume the common root to be e..

Putting e in x^2 - ax + b =0 and (x^2 - px + q ) = 0 and comparing them we get

e^2 - ae + b = e^2 - pe + q

e ( p - a ) = q - b

So, the common root will be....

(q - b)/(p - a ) .........(2)

Putting this value in x^2 - ax + b =0, we get..

(q - b)^2 -a (q - b)(p - a) - b (p - a)^2 = 0

Solving this equation and using equation 1 , we get..

p + b = ap - p - b

2 (p+b) = ap

Hope it works