Math, asked by geethasaravanan15, 9 months ago

ax^3+3x^2-13and 2x^3-5x+a when divided by x-2 leave same remainder. Find value of a

Answers

Answered by Anonymous
5

AnswEr :

\bf{\Large{\underline{\sf{Given\::}}}}

The polynomials ax³ + 3x² -13 and 2x³ - 5x + a when divided by x-2 leave same remainder.

\bf{\Large{\underline{\sf{To\:find\::}}}}

The value of a.

\bf{\Large{\underline{\rm{\orange{Explanation\::}}}}}

\bf{\red{We\:have}\begin{cases}\sf{f(x)=ax^{3} +3x^{2} -13}\\ \sf{g(x)=2x^{3} -5x+a}\end{cases}}

A/q

\leadsto\sf{x-2=0}\\\\\leadsto\sf{\pink{x=2}}

So,

|\Rightarrow\tt{f(2)=g(2)}\\\\\\|\Rightarrow\tt{a.(2)^{3} +3(2)^{2} -13=2(2)^{3} -5(2)+a}\\\\\\|\Rightarrow\tt{a.8+3*4-13=2.8-5*2+a}\\\\\\|\Rightarrow\tt{8a+12-13=16-10+a}\\\\\\|\Rightarrow\tt{8a-1=6+a}\\\\\\|\Rightarrow\tt{8a-a=6+1}\\\\\\|\Rightarrow\tt{7a=7}\\\\\\|\Rightarrow\tt{a\:=\:\cancel{\dfrac{7}{7} }}\\\\\\|\Rightarrow\tt{\red{a=1}}

Thus,

\bigstarThe value of a is 1.

Answered by Anonymous
4

 \huge \boxed{ \fcolorbox{cyan}{grey}{answer : }}

let

 \rm{p1(x) = a {x}^{3} + 3 {x}^{2} - 13}

and

 \rm{p2(x) = 2 {x}^{3} - 5x + a}

 \sf{according \: to \: the \: equation}

 \rm{p1(  2) \: and \: p2( 2)}

 \sf{p1( 2) = a {( 2)}^{2} + 3 {( 2)}^{2} - 13}

 \sf{ 8a + 12 - 13}

 \sf{2 {(  2)}^{2} + 5( 2) + a}

 \sf{ 16 + 10 + a}

then

8a - a = 16 -10 -12 + 13

 \rm{ 7a - 1 =  - 6}

7a = 6+1

7a = 7

a = 1

 \bf{ \huge{ \boxed{ \red{ \tt{a = 1  \: }}}}}}

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