Math, asked by roshni80t, 3 days ago

2. Find the remainder when p(x) = 4x³ +8x²-17x+10 is divided by (2x-1). 11x 50 find the value of a. ​

Answers

Answered by ramjihmi
1

Answer:

P(1/2) = 4

Step-by-step explanation:

P(1/2) = 4(1/2)³+8(1/2)²-17(1/2)+10

= 4×1/8+8×1/4-17/2+10

= 1/2+2-17/2+10

= -16/2+12

= -8+12

P(1/2) =4

Answered by DangerousStudy
12

\large  \red{\underline{\bf{ Question}}}

Find the remainder when p(x) = 4x³+8x²-17x+10 is divided by (2x-1).

\large  \red{\underline{\underline{\bf{Given}}}}

  • p(x) = 4x³+8x²-17x+10
  • g(x) = (2x-1)

\large  \red{\underline{\underline{\bf{To \: Find}}}}

  • The remainder obtained on dividing p(x) by g(x).

\large  \red{\underline{\underline{\bf{Concept}}}}

Remainder Theorem: If p(x) is any polynomial of degree greater than or equal to 1 and p(x) is divided by the linear polynomial (x-a), then the remainder is p(a).

\large  \red{\underline{\underline{\bf{Solution}}}}

\large{\sf{ \implies g(x) = 2x - 1}}

\large{\sf{ \implies 2x - 1 = 0}}

\large{\sf{ \implies 2x  = 1}}

\large \displaystyle{\sf{ \implies x  =  \frac12}}

Now,substitute the value of x in the p(x).

\large{\sf{ \implies p(x) = 4 {x}^{3}  +  {8x}^{2}  - 17x + 10}}

\large \displaystyle{\sf{ \implies p \bigg( \frac12 \bigg) = 4 {  \bigg(\frac12 \bigg)}^{3}  +  {8 \bigg( \frac12 \bigg)}^{2}  - 17  \bigg( \frac{1}{2}  \bigg) + 10}}

\large \displaystyle{\sf{ \implies p \bigg( \frac12 \bigg) = 4 {  \bigg(\frac18 \bigg)}  +  {8 \bigg( \frac14\bigg)} - 17  \bigg( \frac{1}{2}  \bigg) + 10}}

\large \displaystyle{\sf{ \implies p \bigg( \frac12 \bigg) =  \cancel4 \bigg(\frac{1}{\cancel8} \bigg) +  \cancel 8 \bigg( \frac{1}{ \cancel4}\bigg)- \bigg( \frac{17}{2}  \bigg) + 10}}

\large \displaystyle{\sf{ \implies p \bigg( \frac12 \bigg) =   \bigg(\frac{1}{2} \bigg) + 2 \bigg( \frac{1}{ 1}\bigg)- \bigg( \frac{17}{2}  \bigg) + 10}}

\large \displaystyle{\sf{ \implies p \bigg( \frac12 \bigg) =   \bigg(\frac{1}{2} \bigg) +  \bigg( \frac{2}{1}\bigg)- \bigg( \frac{17}{2}  \bigg) + 10}}

\large \displaystyle{\sf{ \implies p \bigg( \frac12 \bigg) = \frac{1 + 4  - 17 + 20}{2} }}

\large \displaystyle{\sf{ \implies p \bigg( \frac12 \bigg) = \frac{8}{2} }}

\large \displaystyle{\sf{ \implies p \bigg( \frac12 \bigg) =  \cancel{\frac{8}{2}} }}

\large \displaystyle{\sf{ \implies p \bigg( \frac12 \bigg) = 4}}

  • Therefore,the remainder obtained on dividing p(x) by g(x) is 4.
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