Question

What is one of the roots of the quadratic equation ${2x}^2-7x+3=0$ by the method of completion of the square? Also, what is the equation obtained after completion of the square?

• A. 6
• B. 3
• C. 12
• D. 13

Answer 1

The correct option is B

3

${2x}^2-7x+3=0$
Dividing by the coefficient of $x^2$, we get
$x^2-\frac{7}{2}x+\frac{3}{2}=0;$
$a=1,b=\frac{7}{2},c=\frac{3}{2}$

Adding and subtracting the square of $\frac{b}{2}=\frac{7}{4}$,

we get,
[$x^2-2\left(\frac{7}{4}\right)x+\left(\frac{7}{4}{)}^2\right]-(\frac{7}{4}{)}^2+\frac{3}{2}$
$=0$

$(x-\frac{7}{4}{)}^2-\frac{25}{16}=0$

Taking Square root, $(x-\frac{7}{4})=(\pm \frac{5}{4})$
Taking positive sign $\frac{5}{4},x=3$
Taking negative sign $\frac{-5}{4},x=\frac{1}{2}$