Answer: 1. [tex]\dfrac{9}{8}[/tex] .
Step-by-step explanation:
The given expression [tex]2x^2-3x+1[/tex]
Using completing the square method.
First, we divide the entire expression by 2 and write in the form of [tex]x^2+bx=c[/tex] , we get
[tex]x^2-\dfrac{3}{2}x+\dfrac{1}{2}[/tex]
Such that [tex]b=\dfrac{3}{2}\ \ \ , c=\dfrac{1}{2}[/tex]
Now add and subtract [tex](\dfrac{b}{2})^2[/tex] on both sides.
[tex](\dfrac{b}{2})^2=(\dfrac{\dfrac{3}{2}}{2})^2\\\\=(\dfrac{3}{2\times2})^2\\\\=(\dfrac{3^2}{4^2})\\\\=\dfrac{9}{8}[/tex]
Here, we add and subtract [tex]\dfrac{9}{8}[/tex] .
Hence, the correct answer is 1. [tex]\dfrac{9}{8}[/tex] .
