The roots of a polynomial function are 2, -1 and ½. Find the polynomial function. Factored form only.
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The roots of a polynomial function are 2, -1 and ½. Find the polynomial function. Factored form only.
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Verified answer
Answer:
f(x) = x³ - ³/₂x² - ⁵/₂x + 1
Step-by-step explanation:
Remember:
The roots of the equation are the values that when substituted equates the polynomial to 0.
These are also the values that intercepts the x-axus with the graph.
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0 = (2-2)(-1+1)(½-½)
⇒ f(x) = (x-2)(x+1)(x-½)
= (x-½)(x²-x-2)
= x³ - ³/₂x² - ⁵/₂x + 1