calculus

[Christodoulou andreas]

y1 curve is y1=x^2+ax+b.Y2 curve is y2=cx-x^2.Both curves have a common tangent line that passes through th point (1,0).Find the a,b,c.
Can somebody help me?

 

[pka]

y1(x)=x<SUP>2</SUP>+ax+b and y2(x)=cx-x<SUP>2</SUP>.
Because (1,0) is on both curves we have 1+a+b=0 and c−1=0.
y1’(x)=2x+a and y2’(x)=c−2x are the slopes of the tangents.
So y1’(1)=y2’(1).
You can solve this system.