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

##### 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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