Find the equation whose roots are \(-\frac{2}{3}\) and 3
A
3x2+11x-6=0
B
3x2+7x+6=0
C
3x2-11x-6=0
D
3x2-7x-6=0
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\(x = -\frac{2}{3} \implies x + \frac{2}{3} = 0\)
\(x = 3 \implies x - 3 = 0\)
\(\implies (x - 3)(x + \frac{2}{3}) = 0\)
\(x^2 - 3x + \frac{2}{3}x - 2 = 0\)
\(x^2 - \frac{7}{3}x - 2 = 0\)
\(3x^2 - 7x - 6 = 0\)
Source: Myschool Past Questions Archive (Record #26609)