If a and b are the roots of the equation $$3x^2 - 5x + 2 = 0$$, then find the value of $$\left(\frac{a}{b}\right) + \left(\frac{b}{a}\right)$$.

$$3x^2 - 5x + 2 = 0$$

this a quadratic equation

$$ax^2 - bx + c = 0$$

here,

a=3

b=-5

c =2

take lcm of 3,2 =6

$$3x^2 - 5x + 2 = 0$$ by doing middle term factorization

$$3x^2 - 3x -2x + 2 = 0$$

$$3x(x-1)  -2(x-1) = 0$$

x-1,3x-2

so, x=1,x=$$\frac{2}{3}$$

 a=1,b=$$\frac{2}{3}$$

$$\left(\frac{a}{b}\right) + \left(\frac{b}{a}\right)$$

$$\left(\frac{1}{\frac{2}{3}}\right) + \left(\frac{\frac{2}{3}}{1}\right)$$

$$\left(\frac{3}{2}\right) + \left(\frac{2}{3}\right)$$

$$\frac{13}{6}$$