Question

If the graph of $f\left(x\right)=2x^3+a{x}^2+bx;a,bϵN$ cuts the x-axis at three distinct points, then minimum value of $(a+b)$ is

• A. 3
• B. 4
• C. 5
• D. 2

Answer 1

The correct option is B 4

$f\left(x\right)=2x^3+a{x}^2+bx$
$f^{\prime }\left(x\right)=6x^2+2ax+b$
Since $f\left(x\right)$ cuts the x-axis three time
$\Rightarrow f^{\prime }\left(x\right)$ posses 2 real roots
$\Rightarrow (2a{)}^2-\mathrm{4.6.}b>0$
$\Rightarrow a^2>6b$
Hence minimum possible value of $a+b=3+1=4,a,bϵN$