Question

answer with steps. no spam . i will mark u brainlist

Answer 1

find the values of p and q by using Remainder Theorem and the rest is in the attachment.

hope it help you.

Answer 2

Given f(x) = x^3 + 2x^2 - 5ax - 7.

Given that f(x) is divided by x + 1, then

= > x + 1 = 0

= > x = -1

Given that p is the remainder on x + 1.

= > f(-1) = p

= > (-1)^3 + 2(-1)^2 - 5a(-1) - 7 = p

= > -1 + 2 + 5a - 7 = p

= > 5a - 6 = p.

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Given g(x) = x^3 + ax^2 - 12x + 6.

Given that g(x) is divided by x - 2, then

= > x - 2 = 0

= > x = 2.

Given that remainder is q on x - 2.

= > f(2) = q

= > (2)^3 + a(2)^2 - 12(2) + 6 = q

= > 8 + 4a - 24 + 6 = q

= > 4a - 10 = q.

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Given 2p + q = 6

= > 2(5a - 6) + (4a - 10) = 6

= > 10a - 12 + 4a - 10 = 6

= > 14a - 22 = 6

= > 14a = 22 + 6

= > 14a = 28

= > a = 2.

Therefore, the value of a = 2.

Hope this helps!