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 :)
