Point of inflection and root of a cubic

Question

I am getting -3 is it right I think k can never be 0 as there is no point of inflection Help

Answer 1

Since you have horizontal dashed lines drawn on the graphing area and the explicit form of the cubic function is not given, you just need to put $k$ equal to the different options and check if that line $y=k$ crosses the graph of the cubic function for exactly three times. Then you should find $k=-3$ as the right answer!

Hope you find this helpful! :)

Answer 2

Only the line $y=-3$ meets the curve at $3$ distinct points.

(Point of inflexion is not a must.)

Answer 3

For understanding purpose:

The curve is composed of infinitely many points with coordinates (x,y)

$f(x)=k$ means $y=k$, or the y-coordinate is $k$

Therefore, you have three points when their y-coordinate is $-3$. This means the three x-coordinates, as their y-coordinate is $-3$, are the three real solutions.

Answer 4

Presently it has one real and two complex (conjugate) roots. If entire curve is pushed up by y=3 units it will have 3 real roots.

So option (A).

Reference to inflection point in title is not entirely necessary. Only how many times the x-axis cuts... that is necessary.