Question

if p(x)=ax³+4x²+3x-4 and g(x)=x³-4x+a leave the same remainder when divided by x-3 find the value of a​

Answer 1

Solution :

$\bf{\large{\underline{\bf{Given\::}}}}}$

If p(x) = ax³ + 4x² + 3x - 4 and g(x) = x³ - 4x + a leaves the same remainder when divided by x - 3.

$\bf{\large{\underline{\bf{To\:find\::}}}}}$

The value of a.

$\bf{\large{\underline{\bf{Explanation\::}}}}}$

We have factor of the given cubic polynomial x - 3

So;

x - 3 = 0

x = 3

$\underline{\underline{\bf{According\:to\:the\:question\::}}}}$

$\longrightarrow\sf{p(x)=g(x)}\\\\\longrightarrow\sf{p(3)=g(3)}\\\\\longrightarrow\sf{a(3)^{3} +4(3)^{2} +3(3)-4=(3)^{3} -4(3)+a}\\\\\longrightarrow\sf{a*27+4*9+9-4=27-12+a}\\\\\longrightarrow\sf{27a+36+5=15+a}\\\\\longrightarrow\sf{27a+41=15+a}\\\\\longrightarrow\sf{27a-a=15-41}\\\\\longrightarrow\sf{26a=-26}\\\\\longrightarrow\sf{a=\cancel{\dfrac{-26}{26} }}\\\\\longrightarrow\sf{\red{a=-1}}$

Thus;

The value of a is -1 .

Answer 2

Given:

p(x)=ax³+4x²+3x-4 and g(x)=x³-4x+a leave the same remainder when divided by x-3.

To find:

The value of a.

Explanation:

we have factor of the given cubic polynomial x - 3.

so;

x - 3 = 0

x = 3

A.T.Q

p(x) + g(x)

p(3) + g(3)

a(3)³ + 4(3)² + 3(3) - 4 = (3)³ - 4(3) + a

a × 27 + 4 × 9 + 9 - 4 = 27 - 12 - a

27a + 36 + 5 = 15 + a

27a - a = 15 - 41

26a = - 26

a = -1

Thus,

The value of a is -1.

silentlover45.❤️