Question

If X+1 factor of 2x3 +ax2 +2abx+1and 2a-3b=4,then find the values of a and b

Answer 1

Step-by-step explanation:

f(x)=2x³+ax²+2abx+1---(1)

2a-3b=4

(2a-4)\3=b---(2)

let x=-1

plug x in eqn (1)

f(-1)=-2+a-2ab+1

=> a-2ab-1=0---(3)

eliminate b

put (2) in (3)

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

a-[(4a²-8a)/3]-1=0

3a-4a²-8a-3=0

4a2+5a+3=0

by using quadratic formula

a=-5/8±(√23 /8)¡

put a in (2)

{2( -5/8±(√23 /8)¡)-4}/3=b

b=(-5/4±(√23/4¡)-4/3=b

b=[(-5/4-4)±(√23/4¡)]/3

b=1/3[(-21/4)±(√23/4¡)

b=(-21/4*3)±(√23 /4*3¡)

b=(-7/4)±(√23 /12¡)

so

a= 5/8±(√23 /8)¡

b=(-7/4)±(√23 /12¡)