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How do you solve #(x-7)(x+2)=0# using the zero product property?

Answer 1

Eva Abramson

Either #x=7# or #x=-2#

Examine the quadratic function represented as the sum of two variables.

#(x-a)(x-b)# with #{a, b} in QQ#

For this product to equal zero either #(x-a) = 0# or #(x-b) = 0#

In the example given in this question #a=7# and #b=-2#

Hence the zeros of #(x-7)(x+2)# are either #7# or #-2#

NB: Checking to see if a quadratic function factorizes in this way is a good place to start when trying to find the zeros for any given function.

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Answer 2

Jace Anderson

To solve the equation ((x - 7)(x + 2) = 0) using the zero product property, follow these steps:

Set each factor equal to zero: [x - 7 = 0] and [x + 2 = 0]
Solve each equation for (x): [x - 7 = 0 \implies x = 7] and [x + 2 = 0 \implies x = -2]
These are the solutions to the equation ((x - 7)(x + 2) = 0) using the zero product property: [x = 7] and [x = -2]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.