Question

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

Answer 1

Hello

If x + 1 is factor then x = - 1
Factor theorum states that p( x ) = 0

Here,

p( x ) = 2x^3 + ax^2 + 2bx + 1
p( - 1 ) = 2(-1)^3 + a(-1)^2 + 2b(-1) + 1
0 = - 2 + a - 2b + 1
0 = - 1 + a - 2b
a - 2b = 1 ------(1)

Now its given that = > 2a - 3b = 4 -----(2)

If we multiply - 2 from (1)

We get , - 2a + 4b = - 2 ------(3)

Add (2) and (3)

We get, b = 2

Then a => a - 2( 2 ) = 1
a - 4 = 1
a = 5

Hope it helps☺!✌