Now in the above quadratic equation the coefficient of x2 is 4. Let us make it unity by dividing the entire quadratic equation by 4.
x2 – 3/4x + 5/4 = 0
x2 – 3/4x = -5/4
Now by taking half of the coefficient of x and then squaring it and adding on both LHS and RHS sides.
Coefficient of x = 3/4
Half of 3/4 = 3/8
Squaring the half of 3/4 = 9/64
Now the LHS term is a perfect square and can be expressed in the form of (a-b) 2 = a2 – 2ab + b2 where a = x and b = 3/8
On simplifying both RHS and LHS we get an equation of following form,
(x ± A)2 = k2
It is observed that the term obtained on RHS is a negative term and taking square root of a negative term will give imaginary roots for the given quadratic equation.
Therefore the given quadratic equation does not has real roots.
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