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 |  91

Solution :-

⇒ 2x2 + x = -4

Dividing both sides of the equation by 2, we get

⇒ x2 + $$\dfrac{1}{2}$$x = 2

⇒ x2 + 2 × x × $$\dfrac{1}{4}$$ = -2

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

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

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

⇒ $$(x + \dfrac{1}{4})^2 = -\dfrac{31}{16}$$

As we know, the square of numbers cannot be negative.

Therefore, there is no real root for the given equation, 2x2 + x + 4 = 0.

Answered by Abhisek | 1 year ago

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