Q. 164.5( 12 Votes )

By using the method of completing the square, show that the equation 2x2 + x + 4 = 0 has no real roots.

Answer :

2x2 + x + 4 = 0

4x2 + 2x + 8 = 0 (multiplying both sides by 2)

4x2 + 2x = - 8

[Adding on both sides]

using a2 + 2ab + b2 = (a + b)2

But cannot be negative for any real value of x

So there is no real value of x satisfying the given equation.

Hence the given equation has no real roots.

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