Answer:
the value of b is 3√5
Explanation:
To find the value of b, we can use the quadratic formula which is given by:
x = (-b ± √(b^2 - 4ac)) / 2a
Here, a = 3, b = b and c = 10.
Let the roots of the equation be α and β, such that α > β.
We know that α - β = 4 1/3 or 13/3.
Using the sum and product of roots formula, we have:
α + β = -b/a ...(1)
αβ = c/a = 10/3 ...(2)
Squaring equation (1), we get:
(α + β)^2 = b^2/a^2
Substituting the values of (1) and (2), we get:
(b^2/9) = (13/3)^2 - 4(10/3)
Solving this equation, we get:
x = -21 or x = 5
Since b is a real number, we can discard the negative value of x. Therefore,
b = √(5*9) = 3√5
Therefore, the value of b is 3√5.