Question

find the value of 'R,if 2x-1 is a factor of the polynomial 6x + Rx- 2
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Answer 1

QuestioN :-

• find the value of R , if 2x-1 is a factor of the polynomial 6x + Rx- 2

SolutioN :-

2x - 1 is a factor of 6x + Rx- 2 , therefore

→ 2x - 1 = 0

→ 2x = 1

→ x = 1/2

Put this in 6x + Rx- 2

→ 6(1/2) + R(1/2) - 2 = 0

→ 3 + R/2 - 2 = 0

→ R/2 + 1 = 0

→ ( R + 2 )2 = 0

→ R + 2 = 0

→ R = - 2

Answer 2

$\:\:\:\: \Large \underline {\sf{Given\::}}$

➟ 2x-1 is a factor of the polynomial 6x + Rx- 2

$\:\:\:\: \large \underline {\sf{To\:Find\::}}$

➟ Value of R

$\:\:\:\: \large \underline {\sf{Solution\::}}$

➟ It is given that 2x - 1 is factor of polynomial , so equate the factor to zero

➟ $\sf 2x\:-\:1\:=\:0$

➟ $\sf 2x\:=\:1$

➟ $\sf x\:=\: \dfrac{1}{2}$

• $\large {\underline{\underline{\sf{Substitue\: value \:of \:x \:in \:polynomial }}}}$

➟ $\sf 6x\:+\:Rx\:-\:2\:=\:0$

➟ $\sf 6(\dfrac{1}{2})\:+\:R(\dfrac{1}{2})\:-\:2 \:=\:0$

➟ $\sf 3 \:+\: \dfrac{R}{2}\:-\:2 \:=\:0$

➟ $\sf \dfrac{R}{2}\:=\:2\:-\:3$

➟ $\sf \dfrac{R}{2}\:=\:-\:1$

➟ $\sf R\:=\:-\:1 \times 2$

$\large\underline{\boxed{\sf{\pink{ R\:=\:-\:2}}}}$

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