SOLUTION: For each function, determine the zeros and their multiplicity. 12. y = (x – 1)2 (2x – 3)3 13. y = (3x – 2)5(x + 4)2 14. y = 4x2(x + 2)3(x + 1)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: For each function, determine the zeros and their multiplicity. 12. y = (x – 1)2 (2x – 3)3 13. y = (3x – 2)5(x + 4)2 14. y = 4x2(x + 2)3(x + 1)      Log On


   



Question 177548: For each function, determine the zeros and their multiplicity.


12. y = (x – 1)2 (2x – 3)3


13. y = (3x – 2)5(x + 4)2



14. y = 4x2(x + 2)3(x + 1)

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The multiplicity of the roots is equal to the exponent of the factor.
12.y=%28x-1%29%5E2%2A%282x-3%29%5E3
2 roots
x-1=0
x=1
3 roots
2x-3=0
2x=3
x=3%2F2
Double root at x=1 (exponent 2), triple root at x=3/2 (exponent 3).
.
.
.
13. y+=+%283x-2%29%5E5%28x%2B4%29%5E2
5 roots
3x-2=0
3x=2
x=2%2F3
2 roots
x%2B4=0
x=-4
.
.
.
14. y+=+4x%5E2%28x+%2B+2%29%5E3%28x+%2B+1%29
2 roots
x=0
3 roots
x%2B2=0
x=-2
1 root
x%2B1=0
x=-1