Using the method of completion of squares find one of the roots of the equation

Question

2 x^{2} - 7 x + 3 = 0

. Also, find the equation obtained after completion of the square.

Options:

A . 6, (x−74)2−2516=0

B . 3, (x−74)2−2516=0

C . 3, (x−72)2−2516=0

D . 13, (x−72)2−2516=0

Answer: Option B
:
B

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

The equation after completing the square is :

(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}

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