Question

Fins the zeros, multiplicity, and effect on the graph of the function in

Answer 1

Answer:

See explanation

Step-by-step explanation:

Zeroe of the function is such velue of x at which f(x)=0.

1. Consider the function $f(x)=-x(3x-2)^2 (x+9)^5.$  

Zeros are:

$-x(3x-2)^2(x+9)^5=0\\ \\x=0\text{ or }x=\dfrac{2}{3}\text{ or }x=-9.$

Zero $x=0$ has multiplicity of 1, zero $x=\dfrac{2}{3}$ has multiplicity of 2, zero $x=-9$ has multiplicity of 5.

At $x=0$ or $x=-9$ the graph of the function crosses the x-axis, at $x=\dfrac{2}{3}$ the graph of the function touches the x-axis.

2. Consider the function $f(x)=x^3+10x^2+25x=x(x^2+10x+25)=x(x+5)^2.$  

Zeros are:

$x(x+5)^2=0\\ \\x=0\text{ or }x=-5.$

Zero $x=0$ has multiplicity of 1, zero $x=-5$ has multiplicity of 2.

At $x=0$ the graph of the function crosses the x-axis, at $x=-5$ the graph of the function touches the x-axis.