Quadratic Challenge
- Thread starter kversel
- Start date
It does not factor. Use the quadratic formula or completing the square.
A quick check to see if a quadratic is factorable or not before you give it a go is to check the discriminant.
The discriminant is \(\displaystyle b^{2}-4ac\). Note, that is what is inside the radical in the quadratic formula. If this is a perfect square, then it IS factorable.
For your case, the discriminant is \(\displaystyle (-1)^{2}-4(1)(-3)=13\). Not a perfect square, so NOT factorable.
Let's check one that is factorable. \(\displaystyle x^{2}-x-2\). The discriminant is \(\displaystyle (-1)^{2}-4(1)(-2)=9\). A perfect square, so it is factorable.
I always thought that was cool little trick to know before you spend time trying to factor and it is not factorable.
A quick check to see if a quadratic is factorable or not before you give it a go is to check the discriminant.
The discriminant is \(\displaystyle b^{2}-4ac\). Note, that is what is inside the radical in the quadratic formula. If this is a perfect square, then it IS factorable.
For your case, the discriminant is \(\displaystyle (-1)^{2}-4(1)(-3)=13\). Not a perfect square, so NOT factorable.
Let's check one that is factorable. \(\displaystyle x^{2}-x-2\). The discriminant is \(\displaystyle (-1)^{2}-4(1)(-2)=9\). A perfect square, so it is factorable.
I always thought that was cool little trick to know before you spend time trying to factor and it is not factorable.
