Question

The equation of tangent at those points where the curve $y=x^2-3x+2$ meets $x$-axis are

• A. $x-y+2=0,x-y-1=0$
• B. $x+y-1=0,x-y-2=0$
• C. $x-y-1=0,x-y=0$
• D. $x-y=0,x+y=0$

Answer 1

The correct option is B $x+y-1=0,x-y-2=0$

solution: $y=x^2-3x+2$

Let the tangent meet the x-axis at point $(x,0)$

$\Rightarrow \frac{dy}{dx}=2x-3$

The tangent passes through point $(x,0)$

$\therefore 0=x^2-3x+2=0$

$\Rightarrow (x-2)(x-1)=0$

$\Rightarrow x=2,x=1$

Case I: when $x=2$

Slope of tangent, ${\frac{dy}{dx}|}_{(2,0)}=2\left(2\right)-3=4-3=1$

$\therefore (x_1,y_1)=(2,0)$

Equation of tangent

$y-y_1=m(x-x_1)$

$\Rightarrow y-0=1(x-2)$

$\Rightarrow x-y-2=0$

Case II: When $x=1$

Slope of tangent ${\frac{dy}{dx}|}_{(2,0)}=2-3=-1$

$\therefore (x_1,y_1)=(1,0)$

Equation of tangent

$y-y_1=m(x-x_1)$

$y-0=-1(x-1)$

$\Rightarrow x+y-1=0$.