Question

Which equation has the solutions x=5+-2(sqrt)7/3

Answer 1

the solution is the last one.

Explanation:

We know that for a second grade equation of the type:

ax^2 + bx + c = 0

The solution will be given by the quadratic formula, which states that:

x1 = [-b + sqrt(b^2 - 4ac)]/2a

x2 = [-b - sqrt(b^2 - 4ac)]/2a

So, according to the solution, we have:

x1 = [-5 + 2sqrt(7)]/3

Then:

2a = 3

-b = 5

b^2 - 4ac = 28

Solving each equation:

a = 2/3

b= -5

c = 9/8

None of the alternatives equals the values obtained before. So we can say that the expression is simplified.

Now we knoe what the first and second equation are wrong because b is not equal to -5.

So we have the other two alternatives, where b=-10. This gives us an idea that maybe, the equation is simplified by two. If that's the case:

then:

2a = 6

b= -10

b^2 - 4ac = 112

Then b=-10, a = 3 and c=-1

So the solution is the last one.