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

Q1.    Find the roots of the following quadratic equations, if they exist, by the method of completing the square:

                (i)    2x^2 - 7x +3 = 0

Answers (1)
D Divya Prakash Singh

Given equation: 2x^2 - 7x +3 = 0

On dividing both sides of the equation by 2, we obtain

\Rightarrow x^2-\frac{7}{2}x+\frac{3}{2} = 0

\Rightarrow (x-\frac{7}{4})^2 + \frac{3}{2} - \frac{49}{16} = 0

\Rightarrow (x-\frac{7}{4})^2 = \frac{49}{16} - \frac{3}{2}

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

\Rightarrow (x-\frac{7}{4}) =\pm \frac{5}{4}

\Rightarrow x =\frac{7}{4}\pm \frac{5}{4}

\Rightarrow x = \frac{7}{4}+\frac{5}{4}\ or\ x = \frac{7}{4} - \frac{5}{4}

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

 

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