First slide
Theory of equations
Question

The curve y=(λ+1)x2+2 intersects the curve y=λx+3 in exactly one point, it λ equals

Easy
Solution

As (λ+1)x2+2=λx+3 has only one solution, so

D = 0

 λ24(λ+1)(1)=0

or λ2+4λ+4=0

or (λ+2)2=0

 λ=2

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