Question

For what value of 'a' is : 2x³ + ax² + 11x +3 exactly divisible by (2x -1)

Answer 1

$\large{\red{\underline{\underline{\bold{Given:-}}}}}$

• Show that 2x³+ax²+11x+3 is exactly divisible by (2x-1)

$\large{\green{\underline{\underline{\bold{To Find:-}}}}}$

• The value of a in the polynomial 2x³+ax²+11x+3 which is divided by (2x-1)

$\large{\blue{\underline{\underline{\bold{Method:-}}}}}$

• Using factor or remainder theorem for the given polynomial

$\{\pink{\underline{\underline{\bold{Solution:-}}}}$

• Let p(x)= 2x³+ax²+11x+3 and f(x)=2x-1
• According to the remainder theorem when p(x) is divided by f(x) then to find value of x substitute f(x) as 0 then 2x-1=0 , x=1/2
• Substitute value of x in p(x)

p(x)=2x³+ax²+11x+3=0

p(1/2)=2(1/2)³+a(1/2)²+11(1/2)+3=0

p(1/2)= 1/4+a/4+11/2+3= 0

11/4+a/4+22/4+12/4=0

11+a+22+12=0

25+a=0

a=-25