Question

If x + k is the GCD of x2 − 2x − 15 and x3 + 27, find the value of k.

Answer 1

Heya your Answer

2 − 2x − 15

= x2 − 5x + 3x − 15 [− 5x + 3x = −2x, − 5x × 3x = −15x2]

= x(x − 5) + 3(x − 5)

= (x − 5) (x + 3)

x3 + 27

= (x)3 + (3)3

= (x + 3) (x2 − 3x + 9) [a3 + b3 = (a + b) (a2 − ab + b2)]

∴GCD of x2 − 2x − 15 and x3 + 27 is x + 3.

It is given that x + k is the G.C.D of x2 − 2x − 15 and x2 + 27.

Comparing x + 3 with x + k, we get k = 3.

Thus, the value of k is 3.

Answer 2

Hey mate

Here is ur answer

(x+k) means x=-k

x2-2x-15

(-k)2-2(-k)-15=0

k2+2k-15=0

k2+5k-3k-15=0

k(k+5)-3(k+5)

(k-3) (k+5)

k=3, -5

x3+a

(-k)3+a

a=k

a = 27 , -125