Question

if x-2 is factor of polynomial f(x)=x^5-3x^4-ax^3+3ax^2+2ax+4 then find the value of 'a'
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Answer 1

Answer:

a = 3/2

Step-by-step explanation:

If x-2 is a factor

Therefore ; x=2

F (x) = x^5 - 3x^4 - ax^3 + 3ax^2 + 2ax + 4

F (2) = (2)^5 - 3(2)^4 - a(2)^3 + 3a(2)^2 + 2a(2) + 4

= 32 - 48 - 8a + 12a + 4a + 4

= 12 - 8a

12 - 8a = 0

8a = 12

a = 12 / 8

a = 3 / 2

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Answer 2

Solution :

$\underline{\bf{Given\::}}}$

x-2 is a factor of polynomial f(x) = x^5 - 3x^4 - ax³ + 3ax² + 2ax + 4.

$\underline{\bf{Explanation\::}}}$

f(x) = 0

∴ x - 2 = 0

x = 2

Now, putting the value of x in given polynomial;

$\mapsto\sf{f(x) = x^{5} -3x^{4} -ax^{3} + 3ax^{2} +2ax +4}\\\\\mapsto\sf{f(2) = (2)^{5} -3(2)^{4} -a(2)^{3} +3a(2)^{2} +2a(2) +4}\\\\\mapsto\sf{ 32 -3 \times 16 -a\times 8 + 3a\times 4 + 4a + 4=0}\\\\\mapsto\sf{32-48 -8a + 12a + 4a + 4=0}\\\\\mapsto\sf{-16 +8a +4=0}\\\\\mapsto\sf{-12 + 8a = 0}\\\\\mapsto\sf{8a = 0+12}\\\\\mapsto\sf{8a=12}\\\\\mapsto\sf{a=\cancel{12/8}}\\\\\mapsto\bf{a=3/2}$

Thus;

The value of a will be 3/2 .