Question

Find the discriminant of quadratic equation
$2 {x}^{2} - 4x + 3 = 0$
and hence find the nature of roots​

Answer 1

Answer:

Discriminant , D = -8 ( D < 0 )

Nature of roots : Imaginary

Note:

★ The general form of a quadratic equation is given by ; ax² + bx + c = 0

★ The discriminant of the given quadratic equation ax² + bx + c = 0 is given by ;

D = b² - 4ac

★ If D > 0 , then the quadratic equation will have real and distinct roots.

★ If D = 0 , then the quadratic equation will have real and equal roots.

★ If D < 0 , then the quadratic equation will have imaginary roots.

Solution:

Here,

The given quadratic equation is ;

2x² - 4x + 3 = 0

Clearly,

a = 2

b = -4

c = 3

Thus,

The discriminant of the given quadratic equation will be given as;

=> D = b² - 4ac

=> D = (-4)² - 4•2•3

=> D = 16 - 24

=> D = -8

=> D < 0

Clearly,

The discriminant of the given quadratic equation is less than zero ( ie ; D < 0 ) , thus it will have imaginary roots .

Hence,

The given quadratic equation has imaginary roots .