Question

Find the quadratic polinomial when divided by x,x-1and x-2 leaves remainder 1,2 and 9 respectively​

Answer 1

Answer:

If  p(x)  is a polynomial with real coefficients and  a∈R , then we can write

p(x)=(x−a)⋅q(x)+r ,

where  q(x)  is a real polynomial and  r∈R . Putting  x=a  on both sides yields  r=p(a) .

Let  p(x)=ax2+bx+c  be the desired quadratic polynomial. Then

1=p(0)=c,2=p(1)=a+b+c,9=p(2)=4a+2b+c .

Hence,  a+b=1  and  4a+2b=8 , or  2a+b=4 . This gives  a=3  and  b=−2 .

The quadratic polynomial is  3x2–2x+1 .  ■

Step-by-step explanation: