Factor the following equation to find its zeros. y = x² - 36

Mathematics

1 answer:

alukav5142 [94]2 years ago

3 0

Answer:

x = 6, x = - 6

Step-by-step explanation:

Given

y = x² - 36

To find the zeros let y = 0, that is

x² - 36 = 0 ← x² - 36 is a difference of squares and factors in general as

a² - b² = (a - b)(a + b), thus

x² - 36 = 0

x² - 6² = 0

(x - 6)(x + 6) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 6 = 0 ⇒ x = - 6

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<em>Additional comments</em>

It is useful to become familiar with the domains of different functions. As we saw above, the reciprocal of 0 is undefined. The square root of a negative number is undefined. The log of a non-positive number is undefined. Trig functions are defined everywhere, but their inverse functions are not. Polynomial functions are defined everywhere, but ratios of polynomials have the same restriction on denominators that we see above.

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