Question 6
2 Marks
The sum of two zeroes of the polynomial x3 – 500×2 + 800x + d is 400. Find
its third zero.

1 thought on “Question 6<br />2 Marks<br />The sum of two zeroes of the polynomial x3 – 500×2 + 800x + d is 400. Find<br />its third zero.<br />”

1. [tex]\underline{\textbf{Given:}}[/tex]

   [tex]\textsf{Sum of two zeroes of the polynomial}\;\mathsf{x^3-500x^2+800x+d\;is\;400}[/tex]

   [tex]\underline{\textbf{To find:}}[/tex]

   [tex]\textsf{The third zero of the polynomial}[/tex]

   [tex]\underline{\textbf{Solution:}}[/tex]

   [tex]\mathsf{Let\;the\;zeroes\;of\;the\;polynomial\;be\;\alpha,\beta\;and\;\gamma}[/tex]

   [tex]\mathsf{As\;per\;given\;data,}[/tex]

   [tex]\mathsf{\alpha+\beta=400}[/tex]

   [tex]\mathsf{Sum\;of\;all\;the\;zeroes=\dfrac{-(-500)}{1}}[/tex]

   [tex]\implies\mathsf{\alpha+\beta+\gamma=500}[/tex]

   [tex]\implies\mathsf{400+\gamma=500}[/tex]

   [tex]\implies\mathsf{\gamma=500-400}[/tex]

   [tex]\implies\boxed{\mathsf{\gamma=100}}[/tex]

   [tex]\therefore\mathsf{The\;third\;zero\;is\;100}[/tex]

   [tex]\underline{\textbf{Answer:}}[/tex]

   [tex]\textsf{Option (a) is correct}[/tex]

   [tex]\underline{\textbf{Find more:}}[/tex]

   If the zeroes of cubic polynomial x3-15×2+74x-120 are the form a,a+b and a+2b for some positive real number, than the value of a and b are​

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