Question

if p(x)=3-4x+x^2,find the value of p(1/2)+p(2)-p(-1)​

Answer 1

Answer:

$\rm \implies p\bigg(\dfrac{1}{2}\bigg) + p(2) - p(-1) = \sf \: \dfrac{ - 31}{4}$

Explanation:

Given polynomial,

$\rm \implies \: p(x) = {x}^{2} - 4x + 3$

Substituting p(½) :-

$\rm \implies \: p \bigg( \frac{1}{2} \bigg) = { \bigg( \frac{1}{2} \bigg) }^{2} - 4 \bigg( \frac{1}{2} \bigg)+ 3$

$\rm = \dfrac{1}{4} - 2 + 3$

$\rm = \dfrac{1 - 8 + 12}{4}$

$= \dfrac{5}{4}$

And also,

Substituting p(2) :-

$\rm \implies \: p(2) = {2}^{2} - 4(2) + 3$

$= 4 - 8 + 3$

$= 7 - 8$

$- 1$

So on, substituting p(-1) :-

$\rm \implies \: p( - 1) = {( - 1)}^{2} - 4( - 1) + 3$

$= 1 + 4 + 3$

$= 8$

Now, finding :-

$\rm = p \bigg( \dfrac{1}{2} \bigg) + p(2) - p( - 1)$

$= \dfrac{5}{4} + ( - 1) - 8$

$= \dfrac{5}{4} - 1 - 8$

$= \dfrac{5}{4} - 9$

$= \dfrac{5 - 36}{4}$

$= \dfrac{ - 31}{4}$

${ \sf{ \underline{ \therefore \: Required \: answer : \dfrac{ - 31}{4} }}}$

Answer 2

$\sf\huge\bold\pink{Answer:}$

$Answer: \\ \rm \implies p\bigg(\dfrac{1}{2}\bigg) + p(2) - p(-1) = \sf \: \dfrac{ - 31}{4} \\ ⟹p(21)+p(2)−p(−1)=4−31 \\ Explanation: \\ Given polynomial \\ \rm \implies \: p(x) = {x}^{2} - 4x + 3 \\ ⟹p(x)=x2−4x+3 \\ Substituting p(½)  \\ \begin{gathered} \rm \implies \: p \bigg( \frac{1}{2} \bigg) = { \bigg( \frac{1}{2} \bigg) }^{2} - 4 \bigg( \frac{1}{2} \bigg)+ 3 \\ \end{gathered} \\ ⟹p(21)=(21)2−4(21)+3 \\ \rm = \dfrac{1}{4} - 2 + 3=41−2+3 \\ \rm = \dfrac{1 - 8 + 12}{4}=41−8+12 \\ = \dfrac{5}{4}=45 \\ And also, \\ \\ Substituting p(2) :- \\ \rm \implies \: p(2) = {2}^{2} - 4(2) + 3 \\ ⟹p(2)=22−4(2)+3 \\ = 4 - 8 + 3=4−8+3 \\ = 7 - 8 \\ =7−8 \\ - 1−1 \\ So on, substituting p(-1) :- \\ \rm \implies \: p( - 1) = {( - 1)}^{2} - 4( - 1) + 3 \\ ⟹p(−1)=(−1)2−4(−1)+3 \\ = 1 + 4 + 3=1+4+3 \\ = 8=8 \\ Now, finding :- \\ \rm = p \bigg( \dfrac{1}{2} \bigg) + p(2) - p( - 1)=p(21)+p(2)−p(−1) \\ = \dfrac{5}{4} + ( - 1) - 8=45+(−1)−8 \\ = \dfrac{5}{4} - 1 - 8=45−1−8 \\ = \dfrac{5}{4} - 9=45−9 \\ = \dfrac{5 - 36}{4}=45−36 \\ = \dfrac{ - 31}{4}=4−31 \\ { \sf{ \underline{ \therefore \: Required \: answer : \dfrac{ - 31}{4} }}} \\ ∴Requiredanswer:4−31$