Question

find the cubic polynomial in "x" which when divided by x-1,x-2 and x-3 leaves remainder 11,22,and 39 respectively ​

Answer 1

We know that the remainder when f(x) is divided by x−α is f(α). If we say that

f(x)=ax2+bx+c

then we have

a×12+b×1+ca+b+ca×22+b×2+c4a+2b+ca×32+b×3+c9a+3b+c=11=11=22=22=37=37(1)(2)(3)

We then have 3 equations in 3 unknowns so we can solve these for a,b,c: (2)−(1):

3a+b=11(4)

(3)−(2):

5a+b=15(5)

(5)−(4):

2a=4a=2

From (4):

3×2+b=11b=5

From (1):

2+5+c=11c=4

And therefore, our quadratic is:

f(x)=2x2+5x+4

hope it helped uhh...

plz.... mark it as BRAINLIEST❤✌