Question

Find the quadratic polynomial when divided by
x, x - 1 and x - 2 leaves remainders 1, 2 and 9
respectively.
27​

Answer 1

Answer:3x²-2x+1

I guess it's enough for you

To solve let $f_{(x)}=ax^2+bx+c$

then use remainder theorem

Being given the remainder for x, x-1, x-2

we must use it

____________________

For x

$f_{(0)}=1$

For x-1

$f_{(1)}=2$

For x-2

$f_{(2)}=9$

For x=0

$f_{(0)}=c$

For x=1

$f_{(1)}=a+b+c$

For x=2

$f_{(2)}=4a+2b+c$

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Solve the linear equation

The solution is $(a,b,c)=(3,-2,1)$

CONCLUTION

∴$f_{(x)}=3x^2-2x+1$