Question

Let p and q be two real numbers with p>0 .Show that the cubic x3

+px+q has exactly one real root .

Answer 1

Thank you for asking this question. Here is your answer:

We will Let f(x) = x³ + px + q

f'(x) = 3x²+p which is greater than zero.

We can conclude form this that f is the increasing function here.

x tends to minus infinity f(x) = - infinity

x tends to infinity f(x)= infinity

So we can say that there is only 1 real root.

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