Question

Consider the polynimial equation x(x-3)(x-6)(x-7)=0. Which of the following are zeros of the equation? Selet all that apply

Answer 1

Answer:

The zeroes of the equation are:

0, 3, 6 and 7

Explanation:

Zeroes of an equation are defined as values of x which make the equation equivalent to zero

Remember that in multiplication, if any of the terms is zero, then the product is equal to zero

The given equation is:

x(x-3)(x-6)(x-7) = 0

Now, we will take each term, equate it to zero and find the corresponding x value which makes this term a zero

For the first term:

x = 0 .................> 1st zero

For the second term:

x-3 = 0 .............> x = 3 ................> 2nd zero

For the third term:

x-6 = 0 ............> x = 6 .................> 3rd zero

For the fourth term:

x-7 = 0 ............> x = 7 ...................> 4th zero

Now, from the above, we can conclude that:

The zeroes of the equation are 0, 3, 6 and 7

Another solution:

Zeroes of an equation are represented graphically as the intersection between the function and the x-axis

Therefore, we can graph the function and get the intersection

The graph is attached below and the intersections are shown to be at:

(0,0) , (3,0) , (6,0) and (7,0)

This means that the zeroes are 0, 3, 6 and 7

Hope this helps :)