Advertisement Remove all ads

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

Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads

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

Advertisement Remove all ads

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

Concept: Solutions of Quadratic Equations by Completing the Square
  Is there an error in this question or solution?

APPEARS IN

NCERT Class 10 Maths
Chapter 4 Quadratic Equations
Exercise 4.3 | Q 1.4 | Page 87
RD Sharma Class 10 Maths
Chapter 4 Quadratic Equations
Exercise 4.4 | Q 5 | Page 26
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×