Question

If the polynomials x cube + ax square +5 and x cube - 2x square +a are divided by (x+2) leave the same remainder, find the value of a. ​

Answer 1

$Let \: p(x) = x^{3} + ax^{2}+5 \: and \\g(x) = x^{3}-2x^{2}+a$

/* According to the problem given */

$If \: p(x) \: divided \: by \: (x+2) \:then \:the \\remainder \: is \: p(-2)$

$If \: g(x) \: divided \: by \: (x+2) \:then \:the \\remainder \: is \: g(-2)$

$p(-2) = g(-2) \: \blue {(Remainders \:are \:same )}$

$\implies (-2)^{3}+a(-2)^{2}+5 = (-2)^{3}-2(-2)^{2}+a$

$\implies -8+4a+5 = -8-8+a$

$\implies -3+4a= -16+a$

$\implies 4a - a = -16+3$

$\implies 3a = -13$

$\implies a = \frac{-13}{3}$

Therefore.,

$\red{ Value \:of \:a } \green {= \frac{-13}{3}}$

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Answer 2

Answer:

Value of a=-13/3

Step-by-step explanation:

that's the correct answer