Question

Find the roots of each of the following quadratic equations by the method of completing the squares
$2x^2-5x+3=0$

• A. $x=2,x=-7$
  
• B. $x=-1,x=3$
• C. $x=1,x=\frac{3}{2}$
• D. $x=1,x=\frac{1}{2}$

Answer 1

Answer: (C)

$x=1,x=\frac{3}{2}$

Dividing the entire equation by 2, we get
$x^2-\frac{5x}{2}+\frac{3}{2}=0$
$(x-\frac{5}{4}{)}^2-\frac{25}{16}+\frac{24}{16}=0$
$(x-\frac{5}{4}{)}^2=\frac{1}{16}$
$x-\frac{5}{4}=\pm \frac{1}{4}$
$x=\frac{5\pm 1}{4}$
Hence
$x=\frac{3}{2}$ and $x=1$