Question

a) If (x + a) is a factor of x4 - a²x2 + 3x - 6.
then the value of a is​

Answer 1

Step-by-step explanation:

If (x+a) is factor of p(x) then,

for x = -a , p(x) will be 0 .

p(x) = x⁴-(a² x²)+3x-6 = 0

=> p(-a) = (-a)⁴ -(a²•-a²)+3(-a) -6 =0

=> a⁴ -a⁴ -3a -6 =0

=> 0 -3a =6

=> a = 6/-3

Thus, a = -2

Answer 2

Answer:

- 2

Step-by-step explanation:

Given : (x + a) is a factor of f(x) = x⁴ - a²x² + 3x - 6

So, x + a = 0

x = - a

And f(- a) = 0

Therefore,

f(- a) = (- a)⁴ - a²(- a)² + 3(- a) - 6

= a⁴ - a²(a²) - 3a - 6

= a⁴ - a⁴ - 3a - 6

0 = - 3a - 6

3a = - 6

a = - 2