1. ## Roots of Equations

One root of the equation x^3+ax^2+7=0 is x=-2. I need to find the value of a.
I tried to do this by using b^2-4ac to find the discriminant, but this didnt work as i dont have a or b just c=7.
I also rearrnaged the equation to give a on its own as -3, but i substituted this back into the equation, but i didnt get 0.

2. Originally Posted by Chez_
One root of the equation x^3+ax^2+7=0 is x=-2. I need to find the value of a.
I tried to do this by using b^2-4ac to find the discriminant, but this didnt work as i dont have a or b just c=7.
I also rearrnaged the equation to give a on its own as -3, but i substituted this back into the equation, but i didnt get 0.

x = -2 is a root. That means when x = -2; then f(x) = 0

$(-2)^3 + (a)(-2)^2 + 7 = 0$

$-8 + a(4) + 7 = 0$

$4a = 1$

$a = \frac{1}{4}$

3. Originally Posted by Chez_
One root of the equation x^3+ax^2+7=0 is x=-2. I need to find the value of a.
I tried to do this by using b^2-4ac to find the discriminant, but this didnt work as i dont have a or b just c=7.
I also rearrnaged the equation to give a on its own as -3, but i substituted this back into the equation, but i didnt get 0.

If the discriminant you are referring to is $b^2 - 4ac$ then you need to look a bit harder at your equation. This discriminant only works for quadratics and you equation is a cubic. It won't work.