If x = -1 and x = -2 are the solutions of the quadratic equation 3x²+ px + q = 0 . then what is the value of (3p — 2q)?

Correct option is C

Given:

The quadratic equation = $$3x^2 + px + q = 0$$​​

The roots of equation are x = -1 and -2

Formula Used:

The roots $$\alpha$$​ and $$\beta$$​ are roots or equation

Then $$\alpha + \beta = -\frac{b}{a}$$​​

​$$(\alpha)(\beta) = \frac{c}{a}$$​​

Solution:

The given equation is $$3x^2 +px +q = 0$$​​

The roots of equation are $$\alpha$$​ = -1 and $$\beta = -2$$​​

Then $$(\alpha +\beta ) (-1)+(-2) = -\frac{b}{a} = - \frac{p}{3}$$​​

​$$-3 = \frac{-p}{3}$$​​

p = 9

The product of roots:

​$$(\alpha)(\beta) = (-1)(-2) =\frac{c}{a} = \frac{q}{3}$$​​

q = 6

The value of 3p -2q = 3(9) - 2(6) = 27 -12 =  15