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Question

The equations of tangent at those points where the curve y = x2 − 3x + 2 meets x-axis are

(a) x − y + 2 = 0 = x − y − 1
(b) x + y − 1 = 0 = x − y − 2
(c) x − y − 1 = 0 = x − y
(d) x − y = 0 = x + y

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Solution

(b) x + y − 1 = 0 = x − y − 2

Let the tangent meet the x-axis at point (x, 0).
Now,
y=x2-3x+2dydx=2x-3The tangent passes through point (x, 0).0=x2-3x+2x-2x-1=0x=2 or x=1Case 1: When x=2:Slope of the tangent, m=dydx2, 0=4-3=1x1, y1=2, 0Equation of the tangent:y-y1=m x-x1y-0=1 x-2x-y-2=0Case 2: When x=1:Slope of the tangent, m=dydx2, 0=2-3=-1x1, y1=1, 0Equation of the tangent:y-y1=m x-x1y-0=-1 x-1x+y-1=0

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