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Find the roots of the following quadratic equations, if they exist, by the method of completing the square 2x^2 – 7x + 3  = 0 - Mathematics

Find the roots of the following quadratic equations, if they exist, by the method of completing the square 2x2 – 7x + 3  = 0

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Solution

2x2 – 7x + 3 = 0

⇒ 2x2 – 7x = - 3

On dividing both sides of the equation by 2, we get

`⇒ x^2 – (7x)/2 = -3/2`

`⇒ x^2 – 2 × x × 7/4 = -3/2`

On adding (7/4)2 to both sides of equation, we get

`⇒ (x)^2 - 2 × x × 7/4 + (7/4)^2 = (7/4)^2 - 3/2`

`⇒ (x - 7/4)^2 = 49/16 - 3/2`

`⇒ (x - 7/4)^2 = 25/16`

`⇒ (x - 7/4) = ± 5/4`

`⇒ x = 7/4 ± 5/4`

`⇒ x = 7/4 + 5/4 or x = 7/4 - 5/4`

`⇒ x = 12/4 or x = 2/4`

⇒ x = 3 or 1/2

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APPEARS IN

NCERT Class 10 Maths
Chapter 4 Quadratic Equations
Exercise 4.3 | Q 1.1 | Page 87
RD Sharma Class 10 Maths
Chapter 4 Quadratic Equations
Exercise 4.4 | Q 2 | Page 26
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