Question

y = bx(x - a)(x-a)(x + b)(x - b)
In the equation above, a and b are positive
constants and a ≠ b. How many distinct x-intercepts
does the graph of the equation in the xy-plane have?

Answer 1

The x-intercepts of an equation are simply the zeros of the equation

The equation $\mathbf{y = bx(x - a)(x -a)(x + b)(x - b)}$ has 4 distinct x-intercepts

The equation is given as:

$\mathbf{y = bx(x - a)(x -a)(x + b)(x - b)}$

Set the equation to 0; i.e. calculate the zeros

$\mathbf{bx(x - a)(x -a)(x + b)(x - b) = 0}$

Divide both sides by constant b

$\mathbf{x(x - a)(x -a)(x + b)(x - b) = 0}$

Split the above equation, as follows

$\mathbf{x= 0\ or\ x - a = 0\ or\ x -a = 0\ or\ x + b = 0\ or\ x - b = 0}$

Solve for x in each of the equation

$\mathbf{x= 0\ or\ x = a\ or\ x = a\ or\ x= -b\ or\ x = b}$

Remove repeated solutions

$\mathbf{x= 0\ or\ x = a\ or\ x= -b\ or\ x = b}$

The count of solutions above is 4

Hence, the equation has 4 distinct x-intercepts

Read more about x-intercepts at:

https://brainly.com/question/3951754