If (x+1) is a factor of 2xcube+axsquare +1 then find the value of a& b given that 2a-3b=4

If (x+1) is a factor of 2xcube+axsquare +1 then find the value of a& b

1.	If (x+1) is a factor of 2xcube+axsquare +1 then find the value of a& b given that 2a-3b=4
Answer» Since {tex}(x + 1){/tex} is a factor of {tex}2x^3 + ax^2 + 2bx + 1{/tex}{tex}\\Rightarrow{/tex}{tex}x = -1{/tex} is a zero of {tex}2x^3 + ax^2 + 2bx + 1{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}2(-1)^3 + a(-1)^2 + 2b(-1) + 1 = 0 {/tex}{tex}\\Rightarrow{/tex}\xa0{tex}a - 2b - 1 = 0{/tex}{tex}\\Rightarrow{/tex}\xa0a - 2b = 1 ...(i)Given that {tex}2a - 3b = 4{/tex} ...(ii)Multiplying equation (i) by 2, we get{tex}2a - 4b = 2{/tex} ...(iii)Subtracting equation (iii) from (ii), we getb = 2Substituting b = 2 in equation (i), we havea - 2(2) = 1{tex}\\Rightarrow{/tex}\xa0a - 4 = 1{tex}\\Rightarrow{/tex}\xa0a = 5Hence, a = 5 and b = 2.