Respuesta :
Answer:
Option A) x=4,12 is correct.
The solution of the given quadratic equation is x=4,12
Step-by-step explanation:
Given equation is in quadratic form
Given quadratic equation is
[tex]0=4x^2-64x+192[/tex]
Rewriting the above equation
[tex]4x^2-64x+192=0[/tex]
Now dividing the equation by 4 we get
[tex]\frac{1}{4}(4x^2-64x+192)=\frac{0}{4}[/tex]
[tex]x^2-16x+48=0[/tex]
For quadratic equation [tex]ax^2+bx+c=0[/tex]
solution [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
where a and b are coefficients of [tex]x^2[/tex] and x respectively, c is a constant
Here a=1, b=-16, c=48
[tex]x=-\frac{(-16)\pm\sqrt{(-16)^2-4(1)(48)}}{2(1)}[/tex]
[tex]=\frac{16\pm\sqrt{16^2-192}}{2}[/tex]
[tex]=\frac{16\pm\sqrt{256-192}}{2}[/tex]
[tex]=\frac{16\pm\sqrt{64}}{2}[/tex]
[tex]x=\frac{16\pm 8}{2}[/tex]
Therefore
[tex]x=\frac{16+8}{2}[/tex] and [tex]x=\frac{16-8}{2}[/tex]
[tex]x=\frac{24}{2}[/tex] and [tex]x=\frac{8}{2}[/tex]
[tex]x=12[/tex] and [tex]x=4[/tex]
Therefore the solution of the given quadratic equation is x=4,12
Option A) x=4,12 is correct.
