Answer:
1. 3 and -5
2. 7
Step-by-step explanation:
The zeros of functions are the x-values when y = 0, i.e the point(s) at which the line crosses the x-axis.
To find the zeros of the given functions, set the function to zero and solve for x.
Question 1
Given function:
[tex]y=5(x-3)(x+5)[/tex]
Set the function to zero:
[tex]\implies 5(x-3)(x+5)=0[/tex]
[tex]\implies \dfrac{5(x-3)(x+5)}{5}=\dfrac{0}{5}\\[/tex]
[tex]\implies (x-3)(x+5)=0[/tex]
Using the Zero Product Property, set each factor equal to zero and solve for x:
[tex]\implies (x-3)=0 \implies x=3[/tex]
[tex]\implies (x+5)=0 \implies x=-5[/tex]
Therefore, the zeros of the function are 3 and -5.
Question 2
Given function:
[tex]y=(x-7)^2[/tex]
Set the function to zero and solve for x
[tex]\implies (x-7)^2=0[/tex]
[tex]\implies \sqrt{(x-7)^2}=\sqrt{0}[/tex]
[tex]\implies x-7=0[/tex]
[tex]\implies x=7[/tex]
Therefore, the zero of the function is 7 (with multiplicity 2).
