find the roots of the following polynomial equation by applying the zero product property .SHOW YOUR SOLUTION
1.(X+3)(X-2)(X+1)(X-1)=0
2.(X+5)(X-5(X+5)(X-1)=0
3.(X+4)²(X-3)³=0
Answers
We know that the Zero Product Property says that,suppose we have ab = 0, then either a = 0, b =0 , or both a and b are equal to 0.
By considering this concept we can solve the given equations .
1.(x+3)(x-2)(x+1)(x-1)=0
In this either (x+3), (x-2), (x+1), or (x-1) = 0
Then for x + 3 = 0,
Therefor x = -3
Like this , we solve x - 2 =0, x + 1 = 0, x - 1 = 0.
So the value of x is
x = -3, 2, -1, 1.
2.(x+5)(x-5)(x+5)(x-1)=0
By using the same concept
x + 5 =0, x - 5 = 0, x+5 = 0, and x - 1 =0
The value of x is ,
x = -5, 5, -5, 1
3.(x+4)^2(x-3)^3=0
when there are exponents:
(x+4)^2 = 0 ,
This is the same as (x+4)(x+4) = 0,
So we also have -4 twice.
Similarly, we also have (x-3) three times, so we have 3 three times.
The value of x is ,
x = -4, -4, 3, 3, 3