Question

If (x+1) is a factor of 2x^3 +ax^2 + 2bx +1, then find the values of a and bgiven that 2a - 3b = 4?

Answer 1

Question :–

• If (x + 1) is a factor of 2x³ +ax² + 2bx + 1 = 0 , then find the values of a and b given that 2a - 3b = 4.

ANSWER :–

➪ a = 5 and b = 2

EXPLANATION :–

GIVEN :–

• A polynomial 2x³ + ax² + 2bx + 1 = 0 have a factor (x + 1) .

• Other relation ⇨ 2a - 3b = 4

TO FIND :–

• Value of a and b .

SOLUTION :–

▪︎ (x + 1) is a factor of given polynomial , So that x = -1 will satisfy the given equation.

▪︎ Put x = -1 in given polynomial –

⇒ 2(-1)³ + a(-1)² + 2b(-1) + 1 = 0

⇒ -2 + a - 2b + 1 = 0

⇒ a - 2b = 1

⇒ a = 1 + 2b ——————eq.(1)

• Now use given condition –

⇒ 2a - 3b = 4

⇒ 2(1 + 2b) - 3b = 4 [using eq.(1)]

⇒ 2 + 4b - 3b = 4

⇒ b = 4 - 2

⇒ b = 2

• Put the value of b in eq.(1) –

⇒ a = 1 + 2(2)

⇒ a = 1 + 4

⇒ a = 5

Hence , a = 5 and b = 2 .