Solve 3x^2-9x+5

The equation y = 3x^2-9x+5 is that of a
parabola.

src="/js/tinymce/js/tinymce/plugins/asciisvg/js/d.svg"
sscr="-.5,4,-2,5,1,1,1,1,1,300,200,func,3x^2-9x+5,null,0,0,,,black,1,none"/>

As
can be seen in the graph provided above, the parabola opens upwards and y is negative only for a
certain set of values of x.

To determine the values for which y =
3x^2-9x+5 is less than 0, determine the roots of the equation 3x^2-9x+5 = 0. The values of x
lying between the roots give a negative value for y =
3x^2-9x+5.

3x^2-9x+5 = 0

The roots of a
quadratic equation ax^2 + bx + c = 0 are given by the formula class="AM">`(-b+-sqrt(b^2 - 4ac))/(2a)`

Here, a = 3,
b = -9 and c = 5, the of the equation are:

class="AM">`(9+-sqrt(81 - 4*3*5))/(6)`

= class="AM">`(9+-sqrt(21))/(6)`

= class="AM">`(9+sqrt(21))/(6)` and class="AM">`(9-sqrt(21))/(6)`

The set of values of x
for which 3x^2-9x+5 < 0 is class="AM">`((9+sqrt(21))/(6),(9-sqrt(21))/(6))`