Question

8. Find the value of a for which x-a is a factor of the polynomial
xpower6-ax power5+x power4-axpower3+3x-a+2​

Answer 1

Answer:

Value of a = -1

Step-by-step explanation:

$Let \: the \: polynomial \\p(x) = x^{6}-ax^{5}+x^{4}-ax^{3}+3x-a+2$

/* If (x-a) is a factor of p(x) then p(a) = 0

$p(a) = a^{6}-a\times a^{5}+a^{4}-a\times a^{3}+3\times a - a + 2 = 0$

$\implies a^{6}-a^{6}+a^{4}-a^{4}+3a-a+2=0$

$\implies 2a+2 =0$

$\implies 2a = -2$

$\implies a = \frac{-2}{2}\\=-1$

Therefore,

Value of a = -1

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Answer 2

The value of a is -1.

Step-by-step explanation:

We need to find the value of a for which (x-a) is a factor of the given polynomial :

$x^6-ax^5+x^4-ax^3+3x-a+2$

Here, (x-a) is a factor of above polynomial. So,

$p(a)=0$

So, putting x = a in above polynomial

$p(a)=a^6-a(a)^5+(a)^4-a(a)^3+3(a)-a+2=0\\\\a^6-a^6+a^4-a^4+3a-a+2=0\\\\2a+2=0\\\\a=-1$

So, the value of a is -1.

Learn more,

Polynomial

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