Question

Show all work to solve 3x2 - x - 2 = 0.

Answer 1

The roots of
`3x^2-x-2=0` are
`\bold{1 \ or \ (-2)/(3)}`

Solution:

Given,
`3x^2-x-2=0`

The given equation is in the format
`ax^2+bx+c=0`

Here, a=3; b=-1; c=-2

The roots of a quadratic function are given by the quadratic formula,

`x=\frac{-b \pm \sqrt{b^(2)-4 a c}}{2 a}`

On substituting the values we get,

`x=\frac{-(-1) \pm \sqrt{(-1)^(2)-4*3*(-2)}}{2*3}`

`x=(+1) \pm √(1-4*3*(-2)))/(6)`

On solving we get,

`x=(+1 \pm √(1+24))/(6)`

`x=(+1 \pm √(25))/(6)`

Square root of 25 is 5,

`x=(+1+5)/(6) \ or \ (-1+5)/(6)`

`x=(6)/(6) \ or \ (-4)/(6)`

`\therefore \ x=1 \ or \ (-2)/(3)`