Answer :

For a quadratic equation: ax^{2} + bx + c = 0,

The roots of equation is given by formula

i) 2x^{2} – 7x + 3 = 0

According to the quadratic formula;

∴ The roots are =

=

=

∴ The roots are 3 and

ii) 2x^{2} + x – 4 = 0

According to the quadratic formula;

=

∴ The roots are =

= =

∴ The roots are =

iii) 4x^{2} + 4√3x + 3 = 0

According to the quadratic formula;

=

∴ The roots are =

=

∴ The roots are

iv) 2x^{2} + x + 4 = 0

According to the quadratic formula;

=

∴ The roots are =

=

This is not possible, Hence the roots do not exists.

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