A day full of math games & activities. Find one near you.

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

Solution:

Given,

(x + 1) is a factor of f(x) = 2x³ + ax² + 2bx + 1,

f(-1) = 0.

If (x + a) is a factor of f(x) = ax² + bx + c, then f(-a) = 0

2(-1)3 + a(-1)2 + 2b (-1) + 1 = 0

By further calculation

-2 + a - 2b + 1 = 0

a - 2b - 1 = 0--------------(1)

2a - 3b = 4

3b = 2a - 4

b = (2a-4/3).

Substituting the value of b in (1), we get,

a - 2(2a-4/3)- 1 = 0

3a - 2(2a - 4) - 3 = 0

3a - 4a + 8 - 3 = 0

-a + 5 = 0

a = 5.

Substituting the value of a in (1),we get

5 - 2b - 1 = 0

2b = 4

b = 2.

a = 5.

b = 2.

Therefore, the values of a and b are 5 and 2, respectively.

✦ Try This: If x+1 is a factor of 2x³ + ax² + 2bx + 1, then find the values of a and b given that 2a-3b = 6

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 3

NCERT Exemplar Class 10 Maths Exercise 3.3 Problem 14

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

Summary:

If x+1 is a factor of 2x³ + ax² + 2bx + 1, then the values of a and b given that 2a-3b = 4 are 5 and 2 respectively.

☛ Related Questions: