Question

the value of 'a' for which (x+a) is the factor of
$x^{2} + ax^{2} -3x+16+a$

Answer 1

Answer :

a = 8

Note:

★ The possible values of the variable for which the polynomial becomes zero are called its zeros .

★ If x - k is a factor of any polynomial p(x) , then x = k is its zero and hence p(k) = 0 .

Solution:

Here,

The given polynomial is ;

x³ + ax² - 3x + 16 + a .

Also,

It is given that , x + a is the factor of the given polynomial .

If x + a = 0 , then

x = - a .

Thus,

x = -a is a zero of the given polynomial and hence at x = -a the given polynomial would become zero .

Thus ,

=> (-a)³ + a(-a)² - 3(a) + 16 + a = 0

=> -a³ + a³ - 3a + a + 16 = 0

=> -2a + 16 = 0

=> -2a = -16

=> a = -16/-2

=> a = 8

Hence ,

Required answer is 8 .