Question

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

Answer 1

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

Answer 2

Given that,

(x + a) is a factor of polynomial x⁴ - a²x² + 3x - 6

equating (x + a) by 0.

➡ x = -a

we know that, when polynomials are divided by it's factors, remainder comes 0.

therefore p(-a) = (-a)⁴ - a²(-a)² + 3(-a) - 6 = 0

➡ a⁴ - a⁴ + 3a - 6 = 0

➡ -3a - 6 = 0

➡ -3a = 6

➡ a = 6/-3

➡ a = -2

VERIFICATION :-

= (2)⁴ - (-2)²(2)² + 3(2) - 6

= 16 - 16 + 6 - 6

= 6 - 6

= 0

hence verified! the value of a = -2