Question

Find the quadratic polynomial in ‘x’ which when divided by (x – 1), (x – 2) and (x – 3) leaves the remainder of 11, 22 and 37 respectively.

Answer 1

Answer:

et f(x) =(x−a)(x−b)(x−1)(x−2)(x−3) (px−a+qx−b+rx−1+sx−2+tx−3) – lab bhattacharjee Jul 28 '17 at 8:05

FOUND! It's P(x)=2x2+5x+4 – Raffaele Jul 28 '17 at 8:50

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