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

2 Answers
Jul 15, 2017

Answer:

Roots are two complex numbers, conjugate of each other.

Explanation:

#2x^2+3x=-3# can be written as #2x^2+3x+3=0#. We may now compare it with general equation #ax^2+bx+c=0#

then Its discriminant is #b^2-4ac# and for #2x^2+3x+3=0# discriminant is #3^2-4xx2xx3=9-24=-15#

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 #-b/(2a)+-sqrt(b^2-4ac)/(2a)#

= #-3/4+-sqrt(-15)/4#

i.e. #-3/4+isqrt15/4# and #-3/4-isqrt15/4#

Jul 15, 2017

Answer:

#"roots are not real"#

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"#