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

x = 1.1 and x = -2.43

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* 3* (-8)}}{2* 3}`.

i.e.
`x=(-4\pm √(16+96))/(6)`.

i.e.
`x=(-4\pm √(112))/(6)`

i.e.
`x=(-4\pm 10.6)/(6)`

i.e.
`x=(-4+10.6)/(6)` and
`x=(-4-10.6)/(6)`

i.e.
`x=(6.6)/(6)` and
`x=(-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.