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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

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

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5964 Points
9 months ago
Dear Student

⇒ 2x^2 + x = -4
Dividing both sides of the equation by 2
⇒ x^2 + 1/2x = 2
⇒ x^2 + 2 × x × 1/4 = -2
By adding (1/4)^2 to both sides of the equation,
⇒ (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
the square of numbers cannot be negative.
Therefore, there is no real root for the given equation,


Thanks

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