Question

A polynomial p(x) when divided by $x^2-3x+2$ leaves remainder 2x-3. Then

• A. p(x) must have a root between 1 and 2
• B. p(x) cannot have a root between 0 and 3
• C. p(x) must have a real root but mayor may not be between 0 and 3
• D. p(x) need not have a real root

Answer 1

Answer: (A)

p(x) must have a root between 1 and 2

$p\left(x\right)=Q\left(x\right).(x^2-3x+2)+(2x-3)$
$p\left(1\right)=-1$
$p\left(2\right)=1$
at least bile root between 1 & 2