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factorise the equation and find the real roots

x^2+3x+4=0

Guest Mar 2, 2017
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You cannot factor it, and it has no real roots!!. However, it has "complex roots" as follows:

 

Solve for x:
x^2 + 3 x + 4 = 0

Subtract 4 from both sides:
x^2 + 3 x = -4

Add 9/4 to both sides:
x^2 + 3 x + 9/4 = -7/4

Write the left hand side as a square:
(x + 3/2)^2 = -7/4

Take the square root of both sides:
x + 3/2 = (i sqrt(7))/2 or x + 3/2 = -(i sqrt(7))/2

Subtract 3/2 from both sides:
x = (0 + i/2) sqrt(7) - 3/2 or x + 3/2 = -(i sqrt(7))/2

Subtract 3/2 from both sides:
Answer: |x = (0 + i/2) sqrt(7) - 3/2        or          x = (0 - i/2) sqrt(7) - 3/2

Guest Mar 2, 2017

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