johnpetertt7 johnpetertt7
  • 18-04-2022
  • Mathematics
contestada

) Find the value of b for which 50y +150 is a factor of y3 – by2 +by+3b. ​

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loneguy
loneguy loneguy
  • 18-04-2022

[tex]f(y) = y^3-by^2+by+3b\\\\\text{Since 50y+150 is a factor of f(y), }\\\\~~~~~f\left ( -\dfrac{150}{50}\right) = 0 \\\\\implies f(-3)=0 \\\\\implies (-3)^3 -b(-3)^2+b(-3)+3b =0\\\\\implies -27-9b-3b+3b=0\\\\\implies -27-9b =0\\\\\implies 9b = -27\\\\\implies b = -\dfrac{27}9\\\\\implies b = -3[/tex]

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