Respuesta :
The roots of the equation are: [tex]x= 4+2i\sqrt{6}[/tex] and [tex]x= 4-2i\sqrt{6}[/tex]
Explanation
Roots means the solutions or the values of x.
Given equation: [tex]\frac{x^2}{4} =2x-10[/tex]
First multiplying both side by 4, we will get...
[tex]x^2= 4(2x-10)\\ \\ x^2= 8x-40\\ \\ x^2-8x+40=0[/tex]
As the above equation is a quadratic equation in form of [tex]ax^2+bx+c=0[/tex] , so [tex]a=1, b=-8[/tex] and [tex]c=40[/tex]
Using quadratic formula...
[tex]x= \frac{-b+/-\sqrt{b^2-4ac} }{2a} \\ \\ x= \frac{-(-8)+/-\sqrt{(-8)^2 -4(1)(40)} }{2(1)}\\ \\ x= \frac{8+/-\sqrt{64-160} }{2}\\ \\ x= \frac{8+/-\sqrt{-96} }{2}\\ \\ x= \frac{8+/-i\sqrt{96} }{2}\\ \\ x= \frac{8+/-4i\sqrt{6} }{2}\\ \\ x= 4+/-2i\sqrt{6}[/tex]
So, the roots of the equation are: [tex]x= 4+2i\sqrt{6}[/tex] and [tex]x= 4-2i\sqrt{6}[/tex]
