Question

What are the roots of 3x2 + 10 = 4x?

Based on the attached image, is the answer either A, B, C or D?

Answer 1

Answer:C

Explanation:

Answer 2

Option C is correct.

roots of the given equation ,
`x =(2\pm i√(26))/(3)`

Explanation:

Given the equation:
`3x^2+10 = 4x`

We can write this equation as:

`3x^2-4x + 10 =0`

A quadratic equation is in the form of
`ax^2+bx+c =0` ......[1] where a,b ,c are the coefficient and x is the variable,

the solution of the equation is given by;

`x = (-b\pm√(b^2-4ac))/(2a)`

On comparing given equation with equation [1] we get;

a = 3 , b = -4 and c =10

So, the solution of the given equation is given by;

`x = (-(-4)\pm√((-4)^2-4(3)(10)))/(2(3))`

or

`x =  (4\pm√((16-120))/(6) = (4\pm√((-104)))/(6) = (4\pm√((-4 * 26)))/(6)`

or

`x =(4\pm2 √((-26)))/(6) = (4\pm2 i√(26))/(6)` [∴
`√(-1) = i`

Simplify:

`x =(2\pm i√(26))/(3)`

therefore, the roots of the given equation are;
`x =(2\pm i√(26))/(3)`