If (x+1) is a factor of …
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Posted by Chanchal Keshariya 6 years, 6 months ago
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Sia ? 6 years, 6 months ago
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} {tex}2(-1)^3 + a(-1)^2 + 2b(-1) + 1 = 0 {/tex}
{tex}\Rightarrow{/tex} {tex}a - 2b - 1 = 0{/tex}
{tex}\Rightarrow{/tex} a - 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 get
b = 2
Substituting b = 2 in equation (i), we have
a - 2(2) = 1
{tex}\Rightarrow{/tex} a - 4 = 1
{tex}\Rightarrow{/tex} a = 5
Hence, a = 5 and b = 2.
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