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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

2 Answers

Harshit Singh
askIITians Faculty 5963 Points
9 months ago
Dear Student

⇒ 2x^2 + x = 4
Dividing both sides of the equation by 2,
⇒ x^2 +x/2 = 2
Now on adding (1/4)^2 to both sides of the equation,
⇒ (x)^2 + 2 × x × 1/4 + (1/4)^2 = 2 + (1/4)^2
⇒ (x + 1/4)^2 = 33/16
⇒ x + 1/4 = ± √33/4
⇒ x = ± √33/4 - 1/4
⇒ x = ± √33-1/4
either
x = √33-1/4 or x = -√33-1/4

Thanks
Ram Kushwah
110 Points
5 months ago
2x²+x-4=0
dividing both sides by 2
x²+x/2-2=0
Or x²+x/2=2
Multiplying both sides by 4
4x²+2x=8
adding both sides (1/2)²=1/4
4x²+2x+1/4=8+1/4
(2x)²+2*(2x)(1/2) +(1/2)² =33/4
(2x+1/2)²=33/4
2x+1/2 = ±√33/4 = ±1/2*√33
2x= ±1/2*√33-1/2
x = ±1/4*√33-1/4
x=(±√33-1)/4
Thus the roots of the equation are:
=(√33-1)/4 and =(-√33-1)/4
Thanks ,pl aprove
 

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