# How do you describe the nature of the roots of the equation #2x^2+3x=-3#?

##### 2 Answers

Roots are two complex numbers, conjugate of each other.

#### Explanation:

then Its discriminant is

As the discriminant is negative, but coefficients of equation are real

te roots of the equation are two complex numbers, conjugate of each other.

The roots are

=

i.e.

#### Explanation:

#"to determine the nature of the roots of a quadratic"#

#"use the "color(blue)"discriminant"#

#•color(white)(x)Delta=b^2-4ac#

#• " if "Delta>0" the roots are real"#

#• " if "Delta=0" the roots are real and equal"#

#• " if "Delta<0" the roots are not real"#

#"rearrange "2x^2+3x=-3" into standard form"#

#"that is " ax^2+bx+c=0#

#"add 3 to both sides"#

#rArr2x^2+3x+3=0#

#"with " a=2,b=3" and " c=3#

#rArrDelta=3^2-(4xx2xx3)=9-24=-15#

#"since "Delta<0" then roots are not real"#