Find the roots of the quadratic equations, if they exist, by the method of completing the square: 2x2 + x – 4 = 0

Asked by Pragya Singh | 1 year ago |  136

1 Answer

Solution :-

⇒ 2x2 + x = 4

Dividing both sides of the equation by 2, we get

⇒ x2 +\( \dfrac{x}{2}\) = 2

Now on adding \(( \dfrac{1}{4})^2\) to both sides of the equation, we get,

\( (x)^2 + 2 × x ×\) \( \dfrac{1}{4}\) + \( ( \dfrac{1}{4})^2\) = 2 + \( ( \dfrac{1}{4})^2\)

⇒ \( (x + \dfrac{1}{4})^2 = \dfrac{33}{16}\)

⇒ \( x + \dfrac{1}{4} = ±\dfrac{\sqrt{33}}{4}\)

⇒ \( x = ±\dfrac{\sqrt{33}}{4}-\dfrac{1}{4}\)

⇒ \( x = \dfrac{\sqrt{33-1}}{4}or\;\dfrac{-\sqrt{33-1}}{4}\)

Answered by Abhisek | 1 year ago

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