What are the solutions to this equation?

Question

anonymous · Answer

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dinnertable · Answer

Since there are no integer factors to factor the equation, you would use the quadratic formula to determine if there is, at all any solutions to the equation.

dinnertable · Answer

In this case, the discriminant is negative, meaning that there are no real solutions.

anonymous · Answer

How could I write the equation to prove that there is no real solution?

dinnertable · Answer

Ok so to start off, I would divide the whole thing by 1/2 to make it easier to work with.
$$1/2x^2 +2x +3 = 0$$
$$x^2 + 4x +6 = 0$$
Now, using the quadratic formula, $$(-b +/- \sqrt{b^2 -4 ac}) / 2a$$
You would substitute each value into it's corresponding variable (a is 1, b is 4, and c is 6)
This would give you $$(-4 +/- \sqrt{16 - 4(1)(6)}) / 2$$

dinnertable · Answer

If the discriminant is less than 0, then there are no real roots. If the discriminant is equal to 0, there is one solution, and if it is greater than 0, there is 2 solutions. (Discriminant is the value under the square root sign in the quadratic formula).

anonymous · Answer

Thanks  so much for the solution and explanation! :D