Question

Find the roots of the quadratic equation ${2x}^2$ - 7$x$ + 3 = 0 by the method of completion of squares.

• A. 6, 3
• B. 3, 1/2
• C. 12, 1/2
• D. 13, 3

Answer 1

The correct option is B

3, 1/2

${2x}^2$-7$x$+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 $\frac{b}{2}$= -$\frac{7}{4}$, (half of coefficient of x)

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

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

Taking Square root, $(x-\frac{7}{4})=(\pm \frac{5}{4}$)

$(x-\frac{7}{4})=(\frac{5}{4}$) $\to$ x = 3

$(x-\frac{7}{4})=-(\frac{5}{4}$) $\to$ x = $\frac{1}{2}$