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

Question

asked Feb 21, 2020 65.5k views

1 Answer

Wcyn · Answer 1 · 2020-02-26T13:05:26+0000

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,

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

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

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