Question

Find the nature of quadratic equation 3x2 + 2x+5= 0

Answer 1

To find the nature of roots we have to find discriminant

Discriminant=b²-4ac

(2)²-4(5)(3)

4-60

-56

Roots are not real

Answer 2

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

Step-by-step explanation:

Given : Quadratic equation $3x^2 + 2x+5= 0$

To find : The nature of quadratic equation ?

Solution :

The nature of quadratic equation is determined by discriminant.

1) $D=b^2-4ac=0$ then roots are real and equal

2) $D=b^2-4ac>0$ then roots are real and unequal.

3) $D=b^2-4ac<0$ then roots are unequal and not real i.e. imaginary.

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

Substitute the value in discriminant,

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

$D=4-60$

$D=-56$

$D<0$

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

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