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# Find the roots of the following quadratic equations, if they exist, by the method of completing the square 2x^2 + x + 4 = 0 - Mathematics

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#### Question

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

#### Solution

2x2 + x + 4 = 0

⇒ 2x2 + x = -4

On dividing both sides of the equation, we get

⇒ x^2 + 1/(2x) = 2

⇒ x^2 + 2 × x × 1/4 = -2

On adding (1/4)2 to both sides of the equation, we get

⇒ (x)^2 + 2 × x × 1/4 + (1/4)^2 = (1/4)^2 - 2

⇒ (x + 1/4)^2 = 1/16 - 2

⇒ (x + 1/4)^2 = -31/16

However, the square of number cannot be negative.

Therefore, there is no real root for the given equation

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#### APPEARS IN

NCERT Solution for Mathematics Textbook for Class 10 (2019 (Latest))