If the line y = x touches the curve y = x 2 + bx + c at a point (1, 1) then

Question

Philoid · Accepted Answer

Given that line y = x touches the curve y = x² + bx + c at a point (1, 1)

Slope of line = 1

Slope of tangent to the curve = 1

⇒ 2x+b = 1

⇒ 2 + b = 1

⇒ b = -1

Putting this and x =1 and y = 1 in the equation of the curve,

1 = 1 -1 + c

⇒ c = 1