Find the roots of the following quadratic equations, if they exist, by the method of completing the square:

(i)


(ii)


(iii)


(iv)


i) 2x2 – 7x +3 =0


Dividing by coefficient of


=


Adding and subtracting the square of


=


=


=


=


=


So,


=


When,


=


When,


=


ii) 2x2 + x – 4 = 0


Dividing by coefficient of


=


Adding and subtracting the square of


=


=


=


=


Taking square root , we get,


=


= x =


x =


iii)


Compare the quadratic equation with


=


=


=


=


Roots of equation are = x =


iv) 2x2 + x + 4


Divide by coefficient of


=


Adding and subtracting the square of


=


=


=


=


Square of a number cannot be negative, Hence roots of following equation do not exist.


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