Question

Find the roots of the following quadratic equations if they exist by the method of completing the square : `3x^(2)-5x+2=0
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Answer 1

Solution

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Correct option is A)

2x2−3x−22=0

⇒  x2−23x−2=0

⇒  Here, a=1,b=−23,c=−2

⇒  x2−23x=2

(2a−b)2=⎝⎜⎜⎜⎛2(1)−(2−3)⎠⎟⎟⎟⎞2=89

Adding 89 on both sides,

⇒  x2−2<

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Answer 2

Find the roots of the following quadratic equations if they exist by the method of completing the square : `3x^(2)-5x+2=0

$x^{2} -\frac{3}{\sqrt{2}}x - 2 = 0$

⇒  Here, a = 1, b = $\frac{3}{\sqrt{2}}$,c = -2

$x^{2} -\frac{3}{\sqrt{2}}x = 2$

$(\frac{-b}{2a})^{2} = (\frac{(\frac{-3}{\sqrt{2}})}{2(1)^{2}}^{2}) = \frac{9}{8}$

Adding $\frac{9}{8}$ on both sides,

$x^{2} - \frac{3}{\sqrt{2}} x + \frac{9}{8} = 2 + \frac{9}{8}$

$(x - \frac{3}{\sqrt[2]{2}} = \frac{5}{\sqrt[2]{2} })$

$x- \frac{3}{\sqrt[2]{2}} = \frac{5}{\sqrt[2]{2}}$ and $x - \frac{3}{\sqrt[2]{2}} = -\frac{5}{\sqrt[2]{2}}$

$x = \sqrt[2]{2}$ and $x = -\frac{1}{\sqrt{2}}$

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