Question

if the polynomial 2x³+ax²+3x-5 and x³+x²-4x+a leave the same remainder when divided by x-2,find the value of a​

Answer 1

Answer:

find the LCM of all numbers

Answer 2

Given,

• a(x) = 2x³+ax²+3x-5
• b(x) = x³+x²-4x+a

It says that:

• While dividing a(x) and b(x) with (x-2), it gives the same remainder.
• (x-2) is a factor of a(x) and b(x).
• 2 is the root of a(x) and b(x).
• a(x) = b(x).

∴ In case of x, applying the value of x (which is 2) to the equation:

$\sf{\implies 2(2)^3+a(2)^2+3(2)-5=(2)^3+(2)^2-4(2)+a}$

$\sf{\implies (2\times8)+(a\times4)+(3\times2)-5 = 8+4-(4\times2)+a}$

$\sf{\implies 16+4a+6-5=8+4-8+a}$

$\sf{\implies 17+4a=4+a}$

$\sf{\implies 4a-a=4-17}$

$\sf{\implies 3a=-13}$

$\sf{\implies a=\dfrac{-13}{3}}$

$\huge{\boxed{\bold{\sf{\therefore a=\dfrac{-13}{3}}}}}$