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blsea [12.9K]
3 years ago
15

What are the real zeros of x^3+4x^2-9x-36

Mathematics
1 answer:
Katyanochek1 [597]3 years ago
6 0

Answer:

x = -4\\x = -3\\x = 3

Step-by-step explanation:

To find the real zeros you must match the function to zero and factor the expression.

We have a polynomial of degree 3.

We try to group the terms to perform the factorization

x ^ 3 + 4x ^ 2-9x-36 = 0\\\\x ^ 2(x + 4) - 9(x + 4) = 0

Now we take (x + 4) as a common factor

(x + 4)(x ^ 2 -9) = 0

If we have an expression of the form (a ^ 2-b ^ 2) we know that this expression is equivalent to:

(a ^ 2-b ^ 2) = (a + b)(a-b)

In this case

a = x\\b = 3

So:

(x ^ 2 -9) = (x + 3)(x-3)

Finally:

x ^ 3 + 4x ^ 2-9x-36 = (x + 4)(x + 3)(x-3) = 0

The solutions are:

x = -4\\x = -3\\x = 3

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