Question

Verify that 3, - 1 and -1/3 are the Zeroes of the Polynomial 3x3-5-11x-3. Check the relationship between Zeroes and their Coefficient.​

Answer 1

Answer with Step - by - Step Explanation:

= p(x) = $3x^3 - 5x^2-11x-3$

(i) If $x$ = 3, then

= p(3) = $3(3)^3 - 5(3)^2 - 11(3) - 3$

= 81 - 45 - 33 - 3

= 81 - 81

= 0

(ii) If $x$ = 1, then

= p(-1) = $3(-1)^3 - 5 (-1)^2 - 11 (-1) -3$

= -3 - 5 + 11 - 3

= -11 +11

= 0

(iii) If $x$ = -1/3, then

= p(-1/3) = $3 (1/3)^3 -5(-1/3)^2-11(-1/3) -3$

= -3/27 - 5/9 + 11/3 - 3

= -1/9 - 2/9 + 11/3 -3

= (-1 - 5 + 33 - 27) / 9

= (-33 + 33) /9

= 0