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

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Solution

2x2 + x – 4 = 0

⇒ 2x2 + x = 4

On dividing both sides of the equation, we get

`⇒ x^2 + x/2 = 2`

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

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

`⇒ (x + 1/4)^2 = 33/16`

`⇒ x + 1/4 = ± sqrt33/4`

`⇒ x = ± sqrt33/4 - 1/4`

`⇒ x = ± sqrt33-1/4`

`⇒ x = (sqrt33-1)/4  `

Concept: Solutions of Quadratic Equations by Completing the Square
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APPEARS IN

NCERT Class 10 Maths
Chapter 4 Quadratic Equations
Exercise 4.3 | Q 1.2 | Page 87
RD Sharma Class 10 Maths
Chapter 4 Quadratic Equations
Exercise 4.4 | Q 4 | Page 26
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