Question

If (x + 2) is a factor of x3+ ax2+ 4bx+ 12and a + b = -4 , find the values of a and b.

Answer 1

Answer :-

Value of a = - 1

Value of b = - 3

Explanation :-

We have,

• x + 2 is a factor of x³ + ax² + 4bx + 12 which means that on dividing of x³ + ax² + 4bx + 12 by x + 2 the remainder is zero.

• a + b = - 4

To find,

• The value of a and b

Solution,

→ P(x) = x³ + ax² + 4bx + 12

→ x + 2 = 0

→ x = - 2

→ P(-2) = x³ + ax² + 4bx + 12 = 0

→ P(-2) = (-2)³ + a(-2)² + 4b(-2) + 12 = 0

→ - 8 + a(4) - 8b + 12 = 0

→ - 8 + 4a - 8b + 12 = 0

→ 4a - 8b + 4 = 0

→ 4(a - 2b + 1) = 0

→ a - 2b + 1 = 0

→ a - 2b = - 1 -------(1)

→ a - 2b = - 1

→ a + b = - 4

⠀(-)⠀(-)⠀ (+)

___________

⠀⠀- 3b = + 3

___________

→ - 3b = 3

→ b = - 1

→ The value of b = - 1

Substitute the value of b in equation (1) :-

→ a - 2b = - 1

→ a - 2(-1) = - 1

→ a + 2 = - 1

→ a = - 1 - 2

→ a = - 3

→ The value of a = - 3