Answer:
[tex]3x^2 -10x - 1 = 0[/tex]
Step-by-step explanation:
We need to find an equation that has the solutions x=(5±2√7)/3
We know that for a polynomial of the type ax^2 + bx + c = 0, the solution to that polynomial is given by the quadratic formula:
[tex]\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex]
In this case, we know that:
-b = 5 → b = -5
2a = 3 → a=3/2
b^2-4ac = 28 → (-5)^2-4(3/2)c = 28 → 25 - 6c = 28 → -6c = 3 → c= -1/2.
Therefore, the equation is:
[tex]\frac{3}{2} x^2 -5x -\frac{1}{2} = 0[/tex]
[tex]3x^2 -10x - 1 = 0[/tex]
