[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
Let's solve for x :
- [tex]27 {x}^{2} + 15x + 10 = 0[/tex]
Using quadratic formula ~
[tex] \boxed{ \frac{ - b \pm \sqrt{b {}^{2 } - 4ac}}{2a} }[/tex]
where,
let's find the roots ~
- [tex] \dfrac{ - 15 \pm \sqrt{( {15})^{2} - (4 \times 27 \times 10)} }{(2 \times 27)} [/tex]
- [tex] \dfrac{ - 15 \pm \sqrt{225 - 1080} }{54}[/tex]
- [tex] \dfrac{ - 15 \pm \sqrt{ - 855} }{54} [/tex]
- [tex] \dfrac{ - 15 \pm3 \sqrt{95} \: i}{54}[/tex]
- [tex] \dfrac{ - 15}{54} \pm \dfrac{3 \sqrt{95} }{54} i[/tex]
- So, the required roots are ~
[tex]x = - \dfrac{5}{18} + \dfrac{3 \sqrt{95} }{54} [/tex]
and
[tex]x = - \dfrac{5}{18} - \dfrac{3 \sqrt{95} }{54} [/tex]
There is no real roots, both the roots are imaginary ~
