Question

What will be the solution of this? `3x^2-6x+8=0`

Answer 1

See a solution process below"

Explanation:

We can use the quadratic equation to solve this problem:

The quadratic formula states:

For `color(red)(a)x^2 + color(blue)(b)x + color(green)(c) = 0`, the values of `x` which are the solutions to the equation are given by:

`x = (-color(blue)(b) +- sqrt(color(blue)(b)^2 - (4color(red)(a)color(green)(c))))/(2 * color(red)(a))`

Substituting:

`color(red)(3)` for `color(red)(a)`

`color(blue)(-6)` for `color(blue)(b)`

`color(green)(8)` for `color(green)(c)` gives:

`x = (-color(blue)(-6) +- sqrt(color(blue)(-6)^2 - (4 * color(red)(3) * color(green)(8))))/(2 * color(red)(3))`

`x = (6 +- sqrt(36 - 96))/6`

`x = 6/6 +- sqrt(-60)/6`

`x = 1 +- sqrt(4 * -15)/6`

`x = 1 +- (sqrt(4)sqrt(-15))/6`

`x = 1 +- (2sqrt(-15))/6`

`x = 1 +- sqrt(-15)/3`

Answer 2

`x=1+-1/3sqrt15i`

Explanation:

`"given a quadratic equation in "color(blue)"standard form"`

`•color(white)(x)ax^2+bx+c=0`

`3x^2-6x+8=0" is in standard form"`

`"with "a=3,b=-6" and "c=8`

`"check the value of the "color(blue)"discriminant"`

`•color(white)(x)Delta=b^2-4ac`

`rArrDelta=(-6)^2-(4xx3xx8)=36-96=-60`

`"since "Delta<0" the equation has no real roots"`

`"but will have 2 "color(blue)"complex conjugate roots"`

`"these can be found using the "color(blue)"quadratic formula"`

`•color(white)(x)x=(-b+-sqrt(Delta))/6`

`rArrx=(6+-sqrt(-60))/6=(6+-2sqrt15i)/6`

`rArrx=6/6+-(2sqrt15i)/6=1+-1/3sqrt15i`