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The questions are in the attachment........... I want the answers of 12 and 13
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12.
Given p(x) = x^3 - ax^2 + 6x - a, g(x) = x - a.
x^2 + 6
------------------------------
x - a) x^3 - ax^2 + 6x - a
x^3 - ax^2
-----------------------------------
6x - a
6x - 6a
------------------------------------
5a.
Therefore Quotient = x^2 + 6 and remainder = 5a
(13).
Let f(x) = 2x^3 + x^2 - ax + 2.
Let g(x) = 2x^3 - 3x^2 - 3x + a
Given that f(x) and g(x), when divided by (x - 2), leaves the same remainder.
f(2) = g(2)
2(2)^3 + (2)^2 - a(2) + 2 = 2(2)^3 - 3(2)^2 - 3(2) + a
16 + 4 - 2a + 2 = 16 - 12 - 6 + a
22 - 2a = -2 + a
-3a = -24
a = 8.
Therefore the value of a = 8.
Hope this helps!
Given p(x) = x^3 - ax^2 + 6x - a, g(x) = x - a.
x^2 + 6
------------------------------
x - a) x^3 - ax^2 + 6x - a
x^3 - ax^2
-----------------------------------
6x - a
6x - 6a
------------------------------------
5a.
Therefore Quotient = x^2 + 6 and remainder = 5a
(13).
Let f(x) = 2x^3 + x^2 - ax + 2.
Let g(x) = 2x^3 - 3x^2 - 3x + a
Given that f(x) and g(x), when divided by (x - 2), leaves the same remainder.
f(2) = g(2)
2(2)^3 + (2)^2 - a(2) + 2 = 2(2)^3 - 3(2)^2 - 3(2) + a
16 + 4 - 2a + 2 = 16 - 12 - 6 + a
22 - 2a = -2 + a
-3a = -24
a = 8.
Therefore the value of a = 8.
Hope this helps!
siddhartharao77:
Gud luck!
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