Question

Solve 9x2 + 12x – 24 = 0 using the quadratic formula. A. x = 7, –1 B. C. D. x = 4, –7

Answer 1

$\bf \qquad \qquad \textit{quadratic formula}\\\\ \begin{array}{lcclll} 9x^2&+12x&-24&=0\\ \uparrow &\uparrow &\uparrow \\ a&b&c \end{array} \qquad \qquad x= \cfrac{ - {{ b}} \pm \sqrt { {{ b}}^2 -4{{ a}}{{ c}}}}{2{{ a}}}$

Answer 2

Answer:

x = 1.1 and x = -2.43

Step-by-step explanation:

We have the quadratic equation, $9x^2+12x-24=0$ i.e. $3x^2+4x-8=0$

Now, we know that,

'The quadratic formula to find the solution of $ax^2+bx+c=0$is given by $x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}$.

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,

$x=\frac{-4\pm \sqrt{4^{2}-4\times 3\times (-8)}}{2\times 3}$.

i.e. $x=\frac{-4\pm \sqrt{16+96}}{6}$.

i.e. $x=\frac{-4\pm \sqrt{112}}{6}$

i.e. $x=\frac{-4\pm 10.6}{6}$

i.e. $x=\frac{-4+10.6}{6}$ and $x=\frac{-4-10.6}{6}$

i.e. $x=\frac{6.6}{6}$ and $x=\frac{-14.6}{6}$

i.e. x = 1.1 and x = -2.43

Thus, the solution of the quadratic equation $9x^2+12x-24=0$ using the quadratic formula is x = 1.1 and x = -2.43.