Question

The value of $k$ for which the equation $|x^2-3x+2|=k$ has three distinct solutions is

• A. $\frac{-1}{4}$
• B. $\frac{1}{4}$
• C. $2$
• D. None of these

Answer 1

The correct option is A $\frac{-1}{4}$

We will first draw the graph of $|x^2-3x+2|$ and y=k

For the graph to have 3 distinct solutions, k must be equal to the vertex of parabola

y coordinate of vertex of parabola =$\frac{4ac-b^2}{4a}$$=\frac{-1}{4}$

$\therefore k=\frac{-1}{4}$