Question

How many time, graph of the polynomial $f\left(x\right)=x^3-1$will intersect $x-$axis.

• A. 0
• B. 1
• C. 2
• D. 4

Answer 1

The correct option is B (1)

Given $f\left(x\right)=x^3-1$,
it intersect $x-$axis when
f (x) = 0
$x^3-1$= 0
$(x-1)(x^2+x+1)=0$
$\Rightarrow (x-1)=0$ or $(x^2+x+1)=0$
$\Rightarrow x=1$ because $(x^2+x+1)=0$ has no real roots.
$\therefore$ it intersect at $x-$axis at only one point $x=1$.
Hence, Option B is correct.