ANSWER:
The roots of [tex]6 x^{2}-9 x+2=0[/tex] are [tex]\frac{9+\sqrt{33}}{4}, \frac{9-\sqrt{33}}{4}[/tex]
SOLUTION:
Given, quadratic equation is [tex]6 x^{2}-9 x+2=0[/tex] --- eqn (1)
We need to find the roots of given quadratic equation using quadratic formula.
Quadratic formula for general quadratic equation [tex]a x^{2}+b x+c=0[/tex] is [tex]X=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]
Here, for eqn (1) a = 6, b= -9 and c = 2
[tex]X=\frac{-(-9) \pm \sqrt{(-9)^{2}-4 \times6 \times 2}}{2 x 2}[/tex]
[tex]X=\frac{9 \pm \sqrt{81-48}}{4}[/tex]
[tex]\begin{array}{l}{X=\frac{9 \pm \sqrt{33}}{4}} \\ {X=\frac{9+\sqrt{33}}{4}, \frac{9-\sqrt{33}}{4}}\end{array}[/tex]
Hence the roots of [tex]6 x^{2}-9 x+2=0[/tex] are [tex]\frac{9+\sqrt{33}}{4}, \frac{9-\sqrt{33}}{4}[/tex]
