Use the zero product property to find the solutions to the equation x² - 9 = 16.

Solution:

In general, we say that zero of a polynomial p(x) is a number c such that p(c) = 0. The zero of the polynomial is obtained by equating it with zero. The value of x at which p(x) becomes zero becomes the root of the equation.

So by equating the given equation to zero we can find the solution. The standard form of quadratic equation is ax² + bx + c = 0

By subtracting 16 from both the sides, we get

⇒ x² – 9 - 16 = 0 

⇒ x² – 25 = 0

Using the equation x² – 25 = 0 in algebraic identity a² –  b² 

⇒ x² – 25 = 0

⇒ x² – 5² = 0

⇒ (x - 5) (x + 5) = 0

Now, we use the zero product property.

We can have two cases:

⇒ x - 5 = 0 or, x + 5 = 0

Hence, we have two solution: x = 5 and x = - 5.

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Use the zero product property to find the solutions to the equation x² - 9 = 16.

Summary:

Using the zero product property the solutions identified to the equation x² - 9 = 16 are x = 5 and x = -5.