Question

Find the roots of x^2/4=2x-10

Answer 1

The roots of the equation are:
`x= 4+2i√(6)` and
`x= 4-2i√(6)`

Step-by-step explanation

Roots means the solutions or the values of x.

Given equation:
`(x^2)/(4) =2x-10`

First multiplying both side by 4, we will get...

`x^2= 4(2x-10)\\ \\ x^2= 8x-40\\ \\ x^2-8x+40=0`

As the above equation is a quadratic equation in form of
`ax^2+bx+c=0` , so
`a=1, b=-8` and
`c=40`

Using quadratic formula...

`x= (-b+/-√(b^2-4ac) )/(2a) \\ \\ x= (-(-8)+/-√((-8)^2 -4(1)(40)) )/(2(1))\\ \\ x= (8+/-√(64-160) )/(2)\\ \\ x= (8+/-√(-96) )/(2)\\ \\ x= (8+/-i√(96) )/(2)\\ \\ x= (8+/-4i√(6) )/(2)\\ \\ x= 4+/-2i√(6)`

So, the roots of the equation are:
`x= 4+2i√(6)` and
`x= 4-2i√(6)`