Question

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

Answer 1

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`

Answer 2

`"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"`