Question

If one of the zero of the polynomial x² + a is -3 then find its other zero.

Answer 1

Explanation:

Since we are given one of the zeroes, we can find the value of a first, and then the value of the other zero.

A zero of the polynomial is the value for the variable such that when it substitutes the variable, the value of the variable is 0.

Hence, we can express the given polynomial as an equation in the following manner:

$x^2 + a = 0$

==> $(-3)^2+ a =0$ [substituting the value of x for given variable]

==> $9+a =0$

∴ $a=-9$

Hence, the polynomial is $x^2-9$.

Now it is a simple and straightforward path from here on to find the other zero/root.

$x^2-9=0$

==> $x^2 - 3^2 = 0$

==> $(x+3)(x-3)=0$ [∵ $a^2 - b^2 = (a+b)(a-b)$]

Hence, since we already know one of the zeroes, the other required zero is 3.

Answer: 3

I hope this helps. :D