Question

Find the value of a for which (x+a) is a factor of the polynomial f(x)= x3+ax2-2x+a+6​

Answer 1

Answer:

the value of a = -2

Step-by-step explanation:

Given polynomial f(x) = $x^{3}+ ax^{2} -2x+a + 6$

   the factor of given polynomial  = x+ a

                                                      ⇒ x = -a

  on substituting x = -a  in f(x) ⇒ f(x) =0

  substitute x = -a in   $x^{3} +ax^{2} -2x+a +6$ =0

                    ⇒  $(-a)^{3} + a (a^{2}) -2a +a +6$ = 0

                    ⇒    $-a^{3} +a^{3} -2(-a) +a +6$= 0  

                    ⇒   3a +6 =0

                    ⇒    3a = - 6

                    ⇒    a = -6 /3 = -2

 value of a = -2  

Answer 2

Answer:

The value of a is -2

Step-by-step explanation:

Given polynomial f(x) = $x^{3}$ + a$x^{2}$ - 2$x$ + a + 6

We have, one factor of given polynomial  = x+ a,

hence, x = -a

on substituting x = -a  in f(x) ⇒ f(x) =0  (since x + a is a factor)

Therefore, f (-a) = $(-a) ^{3}$ + a×$(-a)^{2}$ - 2$(-a)$ + a + 6 = 0

Solving the equation, $(-a) ^{3}$ + a×$a^{2}$ + 2a + a + 6 = 0

i.e, -$a^{3}$ + $a^{3}$ + 2a + a + 6 = 0

3a + 6 =0

Subtracting 6 on both sides,

3a = -6

Dividing 3 on both sides,

a = -6 /3

a = -2