Question

Question 6
2 Marks
The sum of two zeroes of the polynomial x3 - 500x2 + 800x + d is 400. Find
its third zero.
Options
(a) 100
(b) -100
(c) 200
(d) -200​

Answer 1

$\underline{\textbf{Given:}}$

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

$\underline{\textbf{To find:}}$

$\textsf{The third zero of the polynomial}$

$\underline{\textbf{Solution:}}$

$\mathsf{Let\;the\;zeroes\;of\;the\;polynomial\;be\;\alpha,\beta\;and\;\gamma}$

$\mathsf{As\;per\;given\;data,}$

$\mathsf{\alpha+\beta=400}$

$\mathsf{Sum\;of\;all\;the\;zeroes=\dfrac{-(-500)}{1}}$

$\implies\mathsf{\alpha+\beta+\gamma=500}$

$\implies\mathsf{400+\gamma=500}$

$\implies\mathsf{\gamma=500-400}$

$\implies\boxed{\mathsf{\gamma=100}}$

$\therefore\mathsf{The\;third\;zero\;is\;100}$

$\underline{\textbf{Answer:}}$

$\textsf{Option (a) is correct}$

$\underline{\textbf{Find more:}}$

If the zeroes of cubic polynomial x3-15x2+74x-120 are the form a,a+b and a+2b for some positive real number, than the value of a and b are​

https://brainly.in/question/40663788