Question

For which values of a and b, are the zeroes of
$q(x) = {x}^{3} + 2x ^{2} + a$
also the zeroes
of the polynomial
$p(x) = {x}^{5} - x^4 - 4x^3 + 3x^2 + 3x + b$
? Which zeroes of p(x) are
not the zeroes of q(x)?​

Answer 1

Answer:

Since zeroes of q(x) are also the zeroes of p(x), thus, q(x) is the factor of p(x).

The division is in the attachment.

Zeroes of p(x) which are not the zeroes of q(x) are the zeroes of $\sf{g(x) = x^{2} - 3x + 2}$

Zeroes of g(x):

$\sf{x^{2} - 3x + 2 = 0}$

=> $\sf{x^{2} - 2x - x + 2 = 0}$

=> x(x - 2) - 1(x - 2) = 0

=> (x - 1)(x - 2) = 0

=> x = 1 , 2

Thus, 1 and 2 are not the zeroes of q(x)

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