Question

30.1f x+1 and x-1 are factors of
f(x)=x4+3ax+b, then the value
of 3a+2b is(*x to the power
4+3ax+b)
pas​

Answer 1

$\textbf{Given:}$

$\textsf{(x+1) and (x-1) are factors of}\;\mathsf{f(x)=x^4+3ax+b}$

$\textbf{To find:}$

$\textsf{The value of 3a+2b}$

$\textbf{Solution:}$

$\textbf{Factor theorem:}$

$\boxed{\textsf{(x-a) is a factor of f(x) iff f(a)=0}}$

$\textsf{Since (x+1) is factor of f(x),}$

$\mathsf{(-1)^4+3a(-1)+b=0}$

$\mathsf{1-3a+b=0}$

$\implies\mathsf{-3a+b=-1}$-------(1)

$\textsf{Since (x-1) is factor of f(x),}$

$\mathsf{1^4+3a(1)+b=0}$

$\mathsf{1+3a+b=0}$

$\implies\mathsf{3a+b=-1}$-------(2)

$\mathsf{Adding\;(1)\;and\;(2),\;we\;get}$

$\mathsf{2b=-2}$

$\implies\mathsf{b=\dfrac{-2}{2}}$

$\implies\boxed{\mathsf{b=-1}}$

$\mathsf{Put\;b=-1\;in\;(2),\;we\;get}$

$\mathsf{3a+(-1)=-1}$

$\mathsf{3a=-1+1}$

$\mathsf{3a=0}$

$\implies\boxed{\mathsf{a=0}}$

$\textsf{Now,}$

$\textsf{3a+2b=3(0)+2(-1)=0-2=-2}$

$\implies\boxed{\textsf{3a+2b=-2}}$

$\textbf{Find more:}$

If x-3 and x-1/3are factors of ax^2+7x+c then ratio of c:a​please only write proper and valid answer with explanation also

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