Question

find the value of a if xplus a is a factor of x cube plus ax square plus a plus 4​

Answer 1

Question -

• Find the value of a if (x+a) is a factor of

x³+ax²+a+4.

Solution -

Given,

(x+a) is a factor of x³+ax²+a+4

$\therefore x = -a$

Let,

p(x) = x³+ax²+a+4

Putting the value of x = -a

p(-a) =(-a)³ +a(-a)²+a+4

p(-a)= - a³+a³+a+4

p(-a)= a+4

Since,

(x+a) is a factor of x³+ax²+a+4

Therefore Remainder =0

=> a+4=0

=> a= - 4

Verification -

p(-a) =(-a) ³+a(-a)²+a+4

p(-a) = - a³+a³+a+4

p(-a)= a+4

Putting the value of a= - 4

p[-(-4)= - 4+4

p(4)= 0

Since remainder =0

Hence, Verified

Therefore the value of a is - 4