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

Question

asked Aug 13, 2022 226k views

1 Answer

Deepng · Answer 1 · 2022-08-19T07:49:48+0000

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.