Question

If $2a+3b+6c=0,a,b,cϵR$, then the quadratic equation $a{x}^2+bx+c=0$ has

• A. at least one root in [0, 1]
• B. at least one root in [2, 3]
• C. at least one root in (3, 4]
• D. None of the above

Answer 1

The correct option is A

at least one root in [0, 1]

Let $f\left(x\right)=\frac{a{x}^3}{3}+\frac{b{x}^3}{2}+cx+d$ where, f(0) = f(1) = d $\therefore$ f’(x) has atleast one root [0, 1] or $a{x}^2+bx+c$ has atleast one root [0, 1]