Question

consider a polynomial f(x)=ax2+bx+c such that f(0)=4.When f(x) is divided by x+1 then the remainder is 4.Also, when it is divided by x+2, then the reminder is 6
Then
1) a = 3, b = -7
2) a = b = 1, c= 4
Please provide full solution

Answer 1

Answer:

Step-by-step explanation:

ax2+bx+C=4, when x=0, we get C=4

So, f(x)=ax2+bx+4

When f(x) is divided by (x+1), remainder =4

or, f(−1)=4

or a−b+4=4, or a=b …… 1

When f(x) is divided by (x+2), remainder =6

or, f(−2)=6

or 4a−2b+4=6, or 2a−b=1 ……… 2

From equations 1 and 2, we get a=b=1

Thus, a=1,b=1,C=4, or the expression is x2+x+4

Answer 2

hello dear friend hope it help you xd