Question

32. If the remainder on division of x^3 - kx^2 + 13x - 21 by 2x - 1 is-21, find the quotient and the value of k. Hence, find the zeros of the cubic polynomial x^3-kx^2+ 13x.​

Answer 1

Step-by-step explanation:

x^3 - kx^2 + 13x - 21 equation divide (2x-1)

means

x = 1/2 this equation

x^3 - kx^2 + 13x - 21 = 0

(1/2)^3 - k(1/2)^2 + 13/2 - 21 = 0

1/8-k/4+13/2 = 21

k = 53/2

equation x^3 - (53/2)x^2 + 13x - 21

equation x^3 - (53/2)x^2 + 13x - 21 divided by (2x-1)

then reminder = x^2/2 - 13x

x^3 - (53/2)x^2 + 13x - 21 = (2x-1)(x^2/2 - 13x) = 0

2x-1 = 0

x^2/2-13x = 0

x = 1/2

x = 0

x = 26