Respuesta :

mhanifa

Answer:

6x³ - 17x² + 11x - 2

Step-by-step explanation:

The cubic polynomial in general form is:

  • ax³+bx²+cx+d = (x-x1)(x-x2)(x-x3)

zeroes are

  • x1=2, x2=1/3, x3=1/2

then we can get the polynomial as:

  • (x-2)(x-1/3)(x-1/2)=0
  • (x-2)(3x-1)(2x-1)=0
  • (3x²-x-6x+2)(2x-1)=0
  • (3x²-7x+2)(2x-1)=0
  • 6x³-3x²-14x²+7x+4x- 2=0
  • 6x³ - 17x² + 11x - 2= 0

So the required polynomial is:

  • 6x³ - 17x² + 11x - 2

Answer:

f(x) = 6x³ - 17x² + 11x - 2

Step-by-step explanation:

Given the zeros x = 2, x = [tex]\frac{1}{3}[/tex], x = [tex]\frac{1}{2}[/tex] then the factors ar

(x - 2), (x - [tex]\frac{1}{3}[/tex] ), (x - [tex]\frac{1}{2}[/tex] )

By equating the fractional factors to zero we can express them as integer factors, that is

x - [tex]\frac{1}{3}[/tex] = 0 ( multiply through by 3 )

3x - 1 = 0

x - [tex]\frac{1}{2}[/tex] = 0 ( multiply through by 2 )

2x - 1 = 0

Thus the factors are (x - 2), (3x - 1), (2x - 1)

The polynomial is then the product of the factors.

f(x) = (x - 2)(3x - 1)(2x - 1) ← expand last 2 factors using FOIL

     = (x - 2)(6x² - 5x + 1) ← distribute

     = 6x³ - 5x² + x - 12x² + 10x - 2 ← collect like terms

f(x) = 6x³ - 17x² + 11x - 2 ← cubic polynomial

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