Math, asked by prachimpansuriya, 1 month ago

if x+1 is a factor of 2x^3 +ax^2+2bx+1 and 2a-3b=4,then find value of a and b

pls explain ​

Answers

Answered by ItzMeMukku
8

\large\bf{\underline{\underline{Given\: that }}}

\color{red}\boxed{\sf{(x+1)\: is \:a\: factor\: of\: p(x)}}

\large\bf{\underline{\underline{Therefore,}}}

\color{orange}\boxed{\sf{-1 \:is \:a \:zero \:of \:given\:  p(x)}}

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\pink{\bigstar}★ \large\underline{\boxed{\bf\green{p(x) = 2x3 +ax2 +2bx + 1}}}

\textbf{Substituting the value of -1 in the given p(x)}

\large\bf{\underline{\underline{We\: get }}}

\sf{p(x) = 2 * (-1)3 + a * (-1)2 + 2 * b * (-1) + 1}

\sf{-2 + a -2b + 1}

\sf{-1 + a - 2b}

\textbf\color{red}{Or}

\sf{a - 2b = 1}

\sf{2a - 3b = 4}

\sf{a - 2b = 1 ...(1)}

\sf{2a - 3b = 4 ...(2)}

\sf{(1) 2 = 2a - 4b = 2 ...(3)}

\sf{(2) 1 = 2a - 3b = 4 ...(4)}

\sf{(4) - (3) = [ 2a - 2a ] + [ -3b - (-4b) ] = 4-2}

\sf{-3b + 4b = 2}

\large\bf{\underline{\underline{therefore}}}

\color{green}\boxed{\sf{b=2}}

\textbf{substituting the value of b in (3)}

\sf{2a - 4b = 2}

\sf{2a - (4*2) = 2}

\sf{2a - 8 = 2}

\sf{2a = 2 + 8}

\sf{2a = 10}

\sf{a = 10/2}

\tt\color{orchid}{So}

\textbf{We get the values of a and b}

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

\pink{\bigstar}★ \large\underline{\boxed{\bf\green{that\: is: \:a = 5 \:and \:b=2}}}

Thankyou :)

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