Question

if (x+1) and (x-4) are the factors of x cube + x square -px + q. find p and
q.​

Answer 1

QUESTION⤵️

if (x+1) and (x-4) are the factors of x cube + x square -px + q. find p and q.

ANSWER ⤵️

GIVEN THAT:::-

X= -1, 4

${x}^{3} + {x}^{2} - px + q$

PUT X= -1

we get,

$\longrightarrow \: {( - 1)}^{3} + {( - 1)}^{2} - p( - 1) + q$

$\longrightarrow \: ( - 1) + 1 + p + q = 0$

$p + q = 0 = = = = = = =eq.1$

LET P= 0-Q

SO, P= -Q------------------------EQ.3

NOW PUT X= 4

$\longrightarrow {(4)}^{3} + {(4)}^{2} - p \times (4) + q = 0$

$\longrightarrow \: 64 + 16 - 4p + q = 0$

$\longrightarrow \: 80 - 4p + q = 0$

$4p - q = 80 = = = = = = eq.2$

PUT EQ.3 IN EQ. 2

P=-Q

$4( - q) - q = 80$

$- 4q - q = 80$

$- 5q = 80$

$\longrightarrow \: \red{q = - 16}$

THEN PUT THIS Q VALUE IN EQ 1

P-Q=0

$p - ( - 16) = 0$

$p + 16 = 0$

$\longrightarrow \: \red{p = - 16}$

$\huge\star\mathtt\purple{hope \: it \: helps}\star$