Manish's doubt

Algebra Level 2

Once Manish had a doubt. So he asked Rajdeep, the genius his doubt. Seeing the doubt, Rajdeep immediately took a pen and solved his doubt. Manish thanked Rajdeep for his kind help. Can you guess what was Rajdeep's answer if Manish's doubt was as follows:

f ( x ) = a x 3 + b x 2 − 4 x − 3 , w h e r e a a n d b a r e c o n s t a n t s f(x)=a{ x }^{ 3 }+b{ x }^{ 2 }-4x-3,\quad where\quad a\quad and\quad b\quad are\quad constants Given that (x-1) is a factor of f(x)

Find the value of a+b


The answer is 7.

Manish Dash by Manish Dash , 22, India

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3 solutions

Sarthak Rath
Jun 8, 2015

a simple application of remainder theorem... if x-1 is factor of f(x), the f(1) = 0 putting the value, we get a + b -7 = 0 or a + b = 7

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Completely guessed it first try lmao idek how it just came to me ha XD

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Ramiel To-ong
Jun 14, 2015

that's right

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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