Question

if the polynomials ax³ + 3x² -3 and 2x³ -5x + a are divided by (x-4) leaves the same remainder, find the value of a​

Answer 1

$\huge\fcolorbox{red}{cyan}{a\:=\:1}$

Step-by-step explanation:

• f(x) = ax³+3x²-3
• d(x) = 2x³-5x+a
• g(x) = x-4

First Lets Find The Zero of g(x) :-

$x-4=0 \\ => x = 4$

By Remainder Theoram :-

=>f(4) = remainder

=>d(4) = remainder

Since The Remainder is same :-

• =>f(4) = d(4)

$[a\times (4)³] + [3 \times (4)²] - 3 = [2 \times (4)³] - (5 \times 4) + a \\ => (a \times 64) + (3 \times 16) - 3 = (2 \times 64) - 20 + a \\ =>64a + 48 - 3 = 128 - 20 + a \\ => 64a + 45 = 108 + a \\ =>64a - a = 108 - 45 \\ =>63a = 63 \\ =>a = \frac{63}{63} \\ => \boxed{a=1}$

Hope it helped

Answer 2

Answer:

let f(x) =ax^3+3x^2-3

when (f) is dividing by (x-4)

Reminder=f(4)

f(4)=a(4)^3+3(4)^2-3=64a+45

let 'g'(x)=2x^3-5^x+a

when g(x) is dividend by (x-4)

Remainder= g(4)

g(4)=2(4)^3-5(4)=a+108

it is given that f(4)=9(4)

=64a+45a+108

=64a=63

a=1

I hope it will help u