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

Question

Harshit Singh · Answer

Dear Student &rArr; 2x^2 + x = 4 Dividing both sides of the equation by 2, &rArr; x^2 +x/2 = 2 Now on adding (1/4)^2 to both sides of the equation, &rArr; (x)^2 + 2 &times; x &times; 1/4 + (1/4)^2 = 2 + (1/4)^2 &rArr; (x + 1/4)^2 = 33/16 &rArr; x + 1/4 = &plusmn; &radic;33/4 &rArr; x = &plusmn; &radic;33/4 - 1/4 &rArr; x = &plusmn; &radic;33-1/4 either x = &radic;33-1/4 or x = -&radic;33-1/4 Thanks

Ram Kushwah · Answer

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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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

2 Answers

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