if the sum of the roots and product of the roots of ax^3-6x2+2ax-3b=0 is 3&6 respectively.Then find a and b.

To find the values of a and b, we need to use Vieta's formulas, which relate the coefficients of a polynomial to its roots.

For a cubic equation in the form of ax^3 + bx^2 + cx + d = 0, Vieta's formulas state that:

1. The sum of the roots is equal to -b/a.
2. The product of the roots is equal to -d/a.

In the given equation: ax^3 - 6x^2 + 2ax - 3b = 0, the sum of the roots is given as 3, and the product of the roots is given as 6.

So, we have the following equations:

1. -6/a = 3 [Sum of roots]
2. -3b/a = 6 [Product of roots]

Let's solve these equations step by step to find the values of a and b.

Equation 1: -6/a = 3

To find 'a', we can cross-multiply and solve for it:

-6 = 3a
Divide both sides by 3:
-2 = a

So, we have found the value of 'a' to be -2.

Equation 2: -3b/a = 6

Now, substituting the value of 'a' as -2, we have:

-3b/(-2) = 6

To find 'b', we can cross-multiply and solve for it:

-3b = 6 * -2
-3b = -12
Divide both sides by -3:
b = 4

Therefore, the values of 'a' and 'b' are -2 and 4, respectively.

Hence, a = -2, and b = 4.