Question

Find the roots of the following quadratic equations, if they exist, by the method of completing the square. $2x^2-7x+3=0$

• A. The roots of the given quadratic equation are $\frac{1}{3}$ and $1$.
• B. The roots of the given quadratic equation are $\frac{2}{5}$ and $5$.
• C. The roots of the given quadratic equation are $\frac{1}{2}$ and $3$.
• D. The roots of the given quadratic equation are $\frac{2}{7}$ and $4$.

Answer 1

Answer: (C)

The roots of the given quadratic equation are $\frac{1}{2}$ and $3$.

Given equation is $2x^2-7x+3=0$

$\Rightarrow (x^2-\frac{7}{2}x-\frac{7}{2}x+{(-\frac{7}{2})}^2)-{(-\frac{7}{2})}^2+6=0$

$\Rightarrow {(x-\frac{7}{2})}^2-\frac{49}{4}+6=0$

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

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

$\Rightarrow 2x-\frac{7}{2}=\pm \sqrt{\frac{25}{4}}$

$\Rightarrow 2x-\frac{7}{2}=\pm \frac{5}{2}$

$\Rightarrow 2x-\frac{7}{2}=\frac{5}{2}$ or $2x-\frac{7}{2}=-\frac{5}{2}$

$\Rightarrow 2x=\frac{5}{2}+\frac{7}{2}$ or $2x=-\frac{5}{2}+\frac{7}{2}$

$\Rightarrow 2x=6$ or $2x=1$

$\Rightarrow x=3$ or $x=\frac{1}{2}$

Thus, the roots are $3$ and $\frac{1}{2}$.