Quadratic Equation II

The equation can be simplified into $a^2+2a-1=0$ , and then plugged into the quadratic formula to give the answer $\frac { -2\pm \sqrt { { 2 }^{ 2 }+8 } }{ 2 }$ .

That simplifies to give the two solutions $a\approx -2.4142$ and $a\approx 0.4142$ , which sum to give $\boxed{-2}$ .

The quickest way I thought to do it is actually to do 2(-b/2a). This is because he is asking for the sum of the solutions which are (-2+sqrt(8))/2 and (-2-sqrt(8))/2. To make this simpler (and neater), substitute 'a' for sqrt(8). The sum of the solutions will be ((-2-a)+(-2+a))/2, this can be rewritten as (-2-2-a+a)/2. As you can see, the a's, which represent sqrt(8), cancel and we are left with (-4)/2. This way eliminates the need for a calculator and requires much less work.

Use Vieta. Vieta is pure magic.

We don't need to go for such calculations. Just refer these statements.

$ax^2+bx+c=0$ is the general form of quadratic equation.

Sum of roots $= \frac{-b}{a}$

Product of roots $= \frac{c}{a}$

According to question: $a^2+2a-1=0$

So, sum of roots $= \frac{-2}{1}=-2$

Thus, the answer is: $\boxed{-2}$

You can refer my solution.

$a^2+2a+3=4$
$\Rightarrow a^2+2a+1+2=4$
$\Rightarrow (a^2+2a+1)=2$
$\Rightarrow (a+1)^2=2$
$\Rightarrow a= (\sqrt{2}-1)$ or $(-\sqrt{2}-1)$
Adding the two possible values of $a$ , we get
$\sqrt{2}-1-\sqrt{2}-1=(-1-1)=-2$