Question

x+2 and x+4 are the factors 4x^3 +mx^2 + 5x-n, determine the values of m and n.​

Answer 1

GIVEN :–

• x+2 and x+4 are the factors 4x³ + mx² + 5x - n = 0.

TO FIND :–

• Value of m & n = ?

SOLUTION :–

• According to the question x = -2 , -4 are the factors of given equation.

• When x = -2 :–

⇒ 4(-2)³ + m(-2)² + 5(-2) - n = 0

⇒ 4(-8) + 4m - 10 - n = 0

⇒ -32 + 4m - 10 - n = 0

⇒ 4m - n -42 = 0

⇒ 4m - n = 42

⇒ n = 4m - 42 _________eq.(1)

• When x = -4 :–

⇒ 4(-4)³ + m(-4)² + 5(-4) - n = 0

⇒ 4(-64) + 16m - 20 - n = 0

⇒ -256 + 16m - 10 - n = 0

⇒ 16m - n - 266 = 0

• Using eq.(1) –

⇒ 16m - (4m - 42) - 266 = 0

⇒ 16m - 4m + 42- 266 = 0

⇒ 12m = 224

⇒ m = 56/3

• Again using eq.(1) –

⇒ n = 4(56/3) - 42

⇒ n = (224 - 126)/3

⇒ n = 98/3

• Hence , The value of m is 56/3 & n is 98/3 .

Answer 2

Step-by-step explanation:

GIVEN :–

• x+2 and x+4 are the factors 4x³ + mx² + 5x - n = 0.

TO FIND :–

• Value of m & n = ?

SOLUTION :–

• According to the question x = -2 , -4 are the factors of given equation.

• When x = -2 :–

⇒ 4(-2)³ + m(-2)² + 5(-2) - n = 0

⇒ 4(-8) + 4m - 10 - n = 0

⇒ -32 + 4m - 10 - n = 0

⇒ 4m - n -42 = 0

⇒ 4m - n = 42

⇒ n = 4m - 42 _________eq.(1)

• When x = -4 :–

⇒ 4(-4)³ + m(-4)² + 5(-4) - n = 0

⇒ 4(-64) + 16m - 20 - n = 0

⇒ -256 + 16m - 10 - n = 0

⇒ 16m - n - 266 = 0

• Using eq.(1) –

⇒ 16m - (4m - 42) - 266 = 0

⇒ 16m - 4m + 42- 266 = 0

⇒ 12m = 224

⇒ m = 56/3

• Again using eq.(1) –

⇒ n = 4(56/3) - 42

⇒ n = (224 - 126)/3

⇒ n = 98/3

• Hence , The value of m is 56/3 & n is 98/3 .