Question

Please answer the question in attachment

Answer 1

$\large\underline{\sf{Solution-}}$

Given curve is

$\rm :\longmapsto\:f(x) = {x}^{3} - {x}^{2} - x - \dfrac{11}{4}$

Further, it is given that k is a constant real number such that f(x) = k has three real solutions.

Now, we have to find the real value of k, using graphical Method.

If we draw a line y = 2, it cuts the graph of f(x) in one distinct point.

If we draw a line y = 0, it cuts the graph of f(x) in one distinct point.

If we draw a line y = - 2, it cuts the graph of f(x) in one distinct point.

If we draw a line y = - 3, it cuts the graph of f(x) in three distinct points.

Hence, k = - 3, so that f(x) = k has three real solutions.

• So, option (d) is correct

Answer 2

Answer:

$\large\underline{\sf{Solution-}}$

Given curve is

$\rm :\longmapsto\:f(x) = {x}^{3} - {x}^{2} - x - \dfrac{11}{4}$

Further, it is given that k is a constant real number such that f(x) = k has three real solutions.

Now, we have to find the real value of k, using graphical Method.

If we draw a line y = 2, it cuts the graph of f(x) in one distinct point.

If we draw a line y = 0, it cuts the graph of f(x) in one distinct point.

If we draw a line y = - 2, it cuts the graph of f(x) in one distinct point.

If we draw a line y = - 3, it cuts the graph of f(x) in three distinct points.

Hence, k = - 3, so that f(x) = k has three real solutions.

So, option (d) is correct