Question

Solve the quadratic equation 3x^2-9x + 1 = 0
Give your answers to 3 significant figures.​

Answer 1

Given:

The quadratic equation is

`3x^2-9x+1=0`

To find:

The solution of the given equation to 3 significant figures.

Solution:

Quadratic formula for
`ax^2+bx+c=1` is

`x=(-b\pm √(b^2-4ac))/(2a)`

We have,

`3x^2-9x+1=0`

Here,
`a=3,b=-9, c=1`.

`x=(-(-9)\pm √((-9)^2-4(3)(1)))/(2(3))`

`x=(9\pm √(81-12))/(6)`

`x=(9\pm √(69))/(6)`

`x=(9\pm 8.3066)/(6)`

Now,

`x=(9+8.3066)/(6)\text{ and }x=(9-8.3066)/(6)`

`x=(17.3066)/(6)\text{ and }x=(0.6934 )/(6)`

`x=2.884433\text{ and }x=0.115566`

`x\approx 2.884\text{ and }x\approx 0.116`

Therefore, the solutions of the given equation are 2.884 and 0.116.