What are the zeros of the function y=(x+4)(5x-2)

To find the zeros of the function \( y = (x + 4)(5x - 2) \), we need to solve for \( x \) when \( y = 0 \). This is done by setting the equation equal to zero and solving for \( x \):

\[
(x + 4)(5x - 2) = 0
\]

Using the zero-product property, we can set each factor equal to zero:

1. \( x + 4 = 0 \)  
   \[
   x = -4
   \]

2. \( 5x - 2 = 0 \)  
   Solving for \( x \):
   \[
   5x = 2
   \]
   \[
   x = \frac{2}{5}
   \]

Therefore, the zeros of the function are:
\[
x = -4 \quad \text{and} \quad x = \frac{2}{5}
\]

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. How do we factor quadratic functions to find their zeros?
2. What is the significance of the zero-product property in algebra?
3. How can the graph of this function help us understand its zeros?
4. Can you expand \( (x + 4)(5x - 2) \) into standard quadratic form?
5. What happens if one of the factors has no real solutions?

**Tip:** Always check the factored form to ensure it's correct before solving for the zeros!

What are the zeros of the function y = (x + 4)(5x - 2)?

Learn how to find the zeros of the function y = (x + 4)(5x - 2) by applying the zero-product property. This algebra problem involves factoring and solving for x, with a detailed step-by-step solution. Ideal for students in Grades 8-10.

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