Question

If (x – a) is a factor of x³ – ax² + x + 5; the value of a is ______.

पर्याय

• `1/5`

• 5

• `-1/5`

• –5

Answer 1

If (x – a) is a factor of x³ – ax² + x + 5; the value of a is –5.

Explanation:

Let f(x) = x³ – ax² + x + 5

Since x – a is a factor of f(x)

∴ f(a) = 0

`\implies` a³ – a · a² + a + 5 = 0

`\implies` a³ – a³ + a + 5 = 0

`\implies` a + 5 = 0

`\implies` a = –5