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julia-pushkina [17]
2 years ago
7

Need help with question 3 just want to ensure my answer is correct before continuing

History
1 answer:
Blababa [14]2 years ago
8 0

B. -3

The value of a for given polynomial is -3

<h3>Explanation:</h3>

<em>Factor theorem for polynomials,</em>

<u><em>If (x-c) is a factor of polynomial f(x), then f(c)=0</em></u>

Given: x+a is a factor of polynomial 4x^3-13x^2-ax

Let f(x) = 4x^3-13x^2-ax

By Factor theorem, since x+a is a factor of f(x),

(x+a)=[x-(-a)]\\So,\ f(-a)=0

Substituting x=-a in f(x)=0, we get

f(x) = 4x^3-13x^2-ax = 0\\f(-a)= [4(-a)^3]-[13(-a)^2]-[a(-a)] = 0\\(-4a^3-13a^2+a^2)=0\\(-4a^3-12a^2)=0\\-4a^3=12a^2\\\frac{a^3}{a^2} =\frac{12}{-4} \\\\a=(-3)

Therefore, value of a is (-3)

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