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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

  Is there an error in this question or solution?
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APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 10 (2019 (Latest))
Chapter 4: Quadratic Equations
Ex. 4.3 | Q: 1.4 | Page no. 87
 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 4: Quadratic Equations
Ex. 4.4 | Q: 5 | Page no. 26
 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 4: Quadratic Equations
Ex. 4.4 | Q: 5 | Page no. 26
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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 Concept: Solutions of Quadratic Equations by Completing the Square.
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