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Question
If (2x + 1) is a factor of 6x3 + 5x2 + ax – 2 find the value of a.
Solution
Let 2x + 1 = 0, then x = `-(1)/(2)`
Substituting the value of x in f(x),
f(x) = 6x3 + 5x2 + ax – 2
`f(-1/2) = 6(-1/2)^3 + 5(-1/2)^2 + a(-1/2) - 2`
= `6(-1/8) + 5(1/4) + a(-1/2) - 2`
= `-(3)/(4) + (5)/(4) - a/(2) - 2`
= `(-3 + 5 - 2a - 8)/(4)`
= `(-6 - 2a)/(4)`
∴ 2x + 1 is a factor of f(x)
∴ Remainder = 0
∴ `(-6 - 2a)/(4)` = 0
⇒ –6 – 2a = 0
⇒ 2a = 6
⇒ a = 3
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