Question

Which equation has the solutions x=5+-2 square root7/3

Answer 1

`3x^2 -10x - 1 = 0`

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:

`(-b+√(b^2-4ac) )/(2a)`

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:

`(3)/(2) x^2 -5x -(1)/(2) = 0`

`3x^2 -10x - 1 = 0`