Answer:

The nature of the roots are unequal and not real i.e. imaginary roots.

Step-by-step explanation:

Given : Quadratic equation 3x^2 + 2x+5= 03x

2

+2x+5=0

To find : The nature of quadratic equation ?

Solution :

The nature of quadratic equation is determined by discriminant.

1) D=b^2-4ac=0D=b

2

−4ac=0 then roots are real and equal

2) D=b^2-4ac > 0D=b

2

−4ac>0 then roots are real and unequal.

3) D=b^2-4ac < 0D=b

2

−4ac<0 then roots are unequal and not real i.e. imaginary.

In 3x^2 + 2x+5= 03x

2

+2x+5=0 a=3, b=2 and c=5

Substitute the value in discriminant,

D=(2)^2-4(3)(5)D=(2)

2

−4(3)(5)

D=4-60D=4−60

D=-56D=−56

D < 0D<0

The nature of the roots are unequal and not real i.e. imaginary roots.

Step-by-step explanation:

mmh

Answer:

Discriminant - 64

Nature of root - Rational and Unequal

Step-by-step explanation:

Discriminant -

a=3, b=-2, c=-5

b²-4ac

(-2)²-4×3×(-5)

4+60

64

Nature of Root -

Why Rational and Unequal?

Its because 64 is greater than zero and is a perfect square.