Question

Can someone help me please ?!
What are the solutions of the equation
Z^2-6z-27=0

Answer 1

1. 3,9
2. 3,-9
3.-3,9
4.-3,-9

Answer 2

the solution to
\[a z^2 + bz + c = 0\]
is\[\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\]

plug and play.

Answer 3

Or, try to factor \(z^2-6z-27\), that is, write it as a product like this:
\((z-a)\cdot(z-b)=0\). If you can do this, you can split the equation into two easier ones:
\(z-a=0\) and \(z-b=0\), because if one factor of a product is zero, than the whole product is. In this case you can see the solutions are z=a or z=b.

The only question is: how to find a and b?
Well, they are not that hard to find:

The sum of a and b must be -6 (the coefficient of z), so \(a+b=-6\).
The product of a and b must be -27 (the constant), so \(a \cdot b=-27\).

If you think a while about it, you will be able to find a and b.
My guess is, you already know about this method...

Answer 4

So the equation can be rewritten as \((z-9)\cdot (z+3)=0\), see:
\(-9 + 3 = -6\) and \(-9 \cdot 3=-27\).

Can you now see what the right answer is?

Answer 5

Thanks guys

Answer 6

YW!