Question

The quadratic equation $3a{x}^2+2bx+c=0$ has at least one root between 0 and 1 if

• A. a + b + c = 1
• B. a + b + c = 0
• C. 3a + 2ab + c = 0
• D. 6a + 2b = 0

Answer 1

The correct option is B a + b + c = 0

Let $f\left(x\right)=a{x}^3+b{x}^2+cx$
$f\left(0\right)=0=f\left(1\right)\Rightarrow a+b+c=0$