SOLUTION: Find the zeros of each function, state the multiplicity of multiple zeros. 35. y = (2x+3)(x-1)^2

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find the zeros of each function, state the multiplicity of multiple zeros. 35. y = (2x+3)(x-1)^2      Log On


   

Question 114407This question is from textbook Prentice Hall Mathematics Algebra 2
: Find the zeros of each function, state the multiplicity of multiple zeros.
35. y = (2x+3)(x-1)^2 This question is from textbook Prentice Hall Mathematics Algebra 2

Answer by solver91311(24713) About Me  (Show Source):
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If you expanded the right side of the equation you would find that the highest order term would be 2x%5E3. This means that you have a polynomial equation of degree 3, and this means that there are exactly three roots or zeros for this equation.

Expanding the equation a little you get:

y=%282x%2B3%29%28x-1%29%28x-1%29

You should be able to see that y will be zero if and only if:

2x%2B3=0 or
x-1=0 or
x-1=0

Hence, the three roots are x=-3%2F2 or x=1 or x=1. Note that just because two of the roots are equal doesn't change the fact that there are three of them.

Graphically, this is going to look like a sloppy letter 'N'. The graph will cross the x-axis at -3%2F2 and the x-axis will be tangent to a local minimum point at (1, 0). It will also have a local maximum at (-2%2F3,5%2F27). The graph will intercept the y-axis at 3.

graph%28600%2C600%2C-5%2C5%2C-5%2C5%2C%282x%2B3%29%28x-1%29%5E2%29