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vikash chandola Grade:
        

let the parabolas y=x^(2)+ax+band y=x(c-x)touch each other at the point (1,0).Then


a)a= -3             b)b= 1        c)c=2           d)b+c=3

6 years ago

Answers : (2)

Chetan Mandayam Nayakar
312 Points
										

from the first equation, a+b+1=0, from the second equation, c-1=0,c=1,


the quadratic equation in 'x': x^2+ax+b=x(c-x), has only one solution, thus discriminant is zero, (a-c)^2 =8b,c=1,


(a-1)^2 =8b, now combining this with a+b+1=0, and solving we get a=-3,b=2,c=1,b+c=3


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6 years ago
vikas askiitian expert
510 Points
										

y=x^2+ax+b .......1


y=cx-x^2..........2


if both parabola touch each other then they will have a common tangent , we can find dy/dx/solpe  of tangent  from any of the curve 


dy/dx for curve 1=2x +a at 1,0


                        =a+2....eq3


dy/dx for curve 2=c-2x at 1,0


                        =c-2.....eq4


 since 1,0 is point of contact so it will satisfy both the curves


    a+b+2=0....eq5


    c-1=0......eq6


  after solving we get  a=-3,b=1


 

6 years ago
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