Question

Find the value of a, uf x +a us a factor of x⁴-a²x²+3x-a​

Answer 1

Answer:

Value of a is 0.

Step-by-step explanation:

(x + a) is a factor of x⁴ – a²x² + 3x – a.

$\longrightarrow$ x + a = 0

$\longrightarrow$ x = –a

By reminder theorem,

$\longrightarrow$ p(x) = x⁴ – a²x² + 3x – a

$\longrightarrow$ p(a) = –a⁴ – (–a)²a² + 3(–a) – a

$\longrightarrow$ p(a) = –a⁴ + a²a² + 3(–a) – a

As (x + a) is a factor of the given polynomial,

$\longrightarrow$ –a⁴ + a²a² + 3(–a) – a = 0

$\longrightarrow$ –a⁴ + a⁴ – –3a – a

$\longrightarrow$ –4a = 0

$\longrightarrow$ a = 0/4

$\longrightarrow$ a = 0

Value is a is 0.

Therefore, value of a is 0.