for the quadratic equation x^2+4x+2=0 which two option are correct solutions?
1)-3.414 2)-2.764 3)-1.382 4)-0.586 5)1.381 6)1.382 7)3.981 8)4.625
The solution to your equation is
x = -2 ± √2
which of your choices fits that?
(I expect to see two decimal answers, none of them have that, so they messed up)
solution are
x=root2-2=-3.414
and
x=-2-root2=-0.586
To find the solutions for the quadratic equation x^2 + 4x + 2 = 0, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a = 1, b = 4, and c = 2.
Now, let's plug in these values into the quadratic formula and calculate the solutions:
x = (-(4) ± √((4)^2 - 4(1)(2))) / (2(1))
x = (-4 ± √(16 - 8)) / 2
x = (-4 ± √8) / 2
x = (-4 ± 2√2) / 2
x = -2 ± √2
So, the solutions are:
1) x = -2 + √2
2) x = -2 - √2
Let's compare these solutions to the given options:
1) -3.414: Not a solution
2) -2.764: Not a solution
3) -1.382: Not a solution
4) -0.586: Not a solution
5) 1.381: Not a solution
6) 1.382: Not a solution
7) 3.981: Not a solution
8) 4.625: Not a solution
Therefore, neither of the given options is the correct solution. The solutions to the quadratic equation x^2 + 4x + 2 = 0 are x = -2 + √2 and x = -2 - √2.