The figure below is a rhombus. z = [?]
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Check the picture below. So the parabola looks more or less like so.
let's recall that the vertex is half-way between the focus point and the directrix, at "p" units away from both.
Let's notice that the focus point is below the directrix, that means the parabola is vertical, namely the squared variable is the "x", and it also means that it's opening downwards as you see in the picture, namely that "p" is negative, in this case "p" is 1 unit, and thus is -1.
Given:
The function is:
It is given that -1 is a zero of the given function.
To find:
The other zeroes of the given function.
Solution:
If c is a zero of a polynomial P(x), then (x-c) is a factor of the polynomial.
It is given that -1 is a zero of the given function. So, is a factor of the given function.
We have,
Split the middle terms in such a way so that we get (x+1) as a factor.
Again splitting the middle term, we get
For zeroes, .
and
and
and
and
Therefore, the other two zeroes of the given function are and
.