Respuesta :
[tex]\bf \qquad \qquad \textit{quadratic formula}\\\\
\begin{array}{lcclll}
9x^2&+12x&-24&=0\\
\uparrow &\uparrow &\uparrow \\
a&b&c
\end{array}
\qquad \qquad
x= \cfrac{ - {{ b}} \pm \sqrt { {{ b}}^2 -4{{ a}}{{ c}}}}{2{{ a}}}[/tex]
Answer:
x = 1.1 and x = -2.43
Step-by-step explanation:
We have the quadratic equation, [tex]9x^2+12x-24=0[/tex] i.e. [tex]3x^2+4x-8=0[/tex]
Now, we know that,
'The quadratic formula to find the solution of [tex]ax^2+bx+c=0[/tex]is given by [tex]x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}[/tex].
On comparing, we get from the given equation,
a= 3, b= 4 and c= -8
Substituting these values in the given quadratic formula, we get,
[tex]x=\frac{-4\pm \sqrt{4^{2}-4\times 3\times (-8)}}{2\times 3}[/tex].
i.e. [tex]x=\frac{-4\pm \sqrt{16+96}}{6}[/tex].
i.e. [tex]x=\frac{-4\pm \sqrt{112}}{6}[/tex]
i.e. [tex]x=\frac{-4\pm 10.6}{6}[/tex]
i.e. [tex]x=\frac{-4+10.6}{6}[/tex] and [tex]x=\frac{-4-10.6}{6}[/tex]
i.e. [tex]x=\frac{6.6}{6}[/tex] and [tex]x=\frac{-14.6}{6}[/tex]
i.e. x = 1.1 and x = -2.43
Thus, the solution of the quadratic equation [tex]9x^2+12x-24=0[/tex] using the quadratic formula is x = 1.1 and x = -2.43.
