Find a polynomial f(x) of degree 4 that has the following zeros.
0, -5, 8, -2

The polynomial of the function degree '4'

x⁴ - x³ -46 x² -80x =0

Step-by-step explanation:

Explanation:-

Given zeros are 0 ,-5,8,-2

x =0 , x=-5 ,x=8 and x=-2

(x-0) , ( x+5) , (x-8) and (x+2)

The polynomial function with degree '4'

(x-0)(x-(-5)(x-8)(x-(-2) =0

x ( x+5) (x-8) (x+2) =0

(x² +5x)(x-8)(x+2) =0

(x³ -8 x²+5x² -40 x)(x+2) =0

( x³ -3 x² - 40 x) (x +2) =0

x⁴ + 2 x³ - 3 x³- 6 x²-40 x²- 80 x =0

x⁴ - x³ -46 x² -80x =0

Final -

The polynomial of the function degree '4'

x⁴ - x³ -46 x² -80x =0    

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step-by-step explanation: