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

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x + y − 1 = 0 = x − y − 2 Let the tangent meet the x-axis at point (x, 0). Now, y = x^2 - 3x + 2 \Rightarrow dy/dx = 2x - 3 	ext { The tangent passes through point (x, 0) }. 	herefore 0 = x^2 - 3x + 2 \Rightarrow \left( x - 2 ight)\left( x - 1 ight) = 0 \Rightarrow x = 2 \ or \ x = 1 	ext { Case 1: When } x=2: 	ext { Slope of the tangent },m= \left( dy/dx ight)_\left( 2, 0 ight) =4-3=1 	herefore \left( x_1 , y_1 ight) = \left( 2, 0 ight) 	ext { Equation of the tangent }: y - y_1 = m \left( x - x_1 ight) \Rightarrow y - 0 = 1 \left( x - 2 ight) \Rightarrow x - y - 2 = 0 	ext { Case 2: When } x=1: 	ext { Slope of the tangent },m= \left( dy/dx ight)_\left( 2, 0 ight) =2-3=-1 	herefore \left( x_1 , y_1 ight) = \left( 1, 0 ight) 	ext { Equation of the tangent }: y - y_1 = m \left( x - x_1 ight) \Rightarrow y - 0 = - 1 \left( x - 1 ight) \Rightarrow x + y - 1 = 0

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