Given:
The quadratic equation is
[tex]3x^2-9x+1=0[/tex]
To find:
The solution of the given equation to 3 significant figures.
Solution:
Quadratic formula for [tex]ax^2+bx+c=1[/tex] is
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
We have,
[tex]3x^2-9x+1=0[/tex]
Here, [tex]a=3,b=-9, c=1[/tex].
[tex]x=\dfrac{-(-9)\pm \sqrt{(-9)^2-4(3)(1)}}{2(3)}[/tex]
[tex]x=\dfrac{9\pm \sqrt{81-12}}{6}[/tex]
[tex]x=\dfrac{9\pm \sqrt{69}}{6}[/tex]
[tex]x=\dfrac{9\pm 8.3066}{6}[/tex]
Now,
[tex]x=\dfrac{9+8.3066}{6}\text{ and }x=\dfrac{9-8.3066}{6}[/tex]
[tex]x=\dfrac{17.3066}{6}\text{ and }x=\dfrac{0.6934 }{6}[/tex]
[tex]x=2.884433\text{ and }x=0.115566[/tex]
[tex]x\approx 2.884\text{ and }x\approx 0.116[/tex]
Therefore, the solutions of the given equation are 2.884 and 0.116.
