Question

A polynomial function has zeros at 5/2 (multiplicity 2), 3 (multiplicity 1), and 0 (multiplicity 4). Write a function in standard form that could represent this function

Answer 1

Answer:

-75 x^4 + 85 x^5 - 32 x^6 + 4 x^7

Step-by-step explanation:

$(x-5/2)^{2}(x-3)(x-0)^4 =0\\(2x-5)^{2}(x-3)(x)^4 =0$

Expand and get

-75 x^4 + 85 x^5 - 32 x^6 + 4 x^7

Answer 2

The standard form will be  $X^4(x^4-7x^3+12x^2-\dfrac{35x}{2} +\dfrac{25x^2}{4} +\dfrac{25}{4} =0$

What will be the standard form of the given expression?

The given expression is

$(x-\dfrac{5}{2})^2(x-1)^2(x-0)^4=0$

$(x^2-5x+\frac{25}{4} )(x^2-2x+1)(x^4)=0$

$(x^4-2x^3+x^2-5x^3+10x^2-5x+\dfrac{25x^2}{4} -\dfrac{50}{4} x+\dfrac{25}{4} ) x^4=0$

$X^4(x^4-7x^3+12x^2-\dfrac{35x}{2} +\dfrac{25x^2}{4} +\dfrac{25}{4} =0$

Thus the standard form will be  

$X^4(x^4-7x^3+12x^2-\dfrac{35x}{2} +\dfrac{25x^2}{4} +\dfrac{25}{4} =0$

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