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let p and q be two real numbers with p is greater than zero show that cubic x cube + px + q is exactly one real root

let p and q be two real numbers with p is greater than zero show that cubic x cube + px + q is exactly one real root

Grade:10

1 Answers

Aditya Gupta
2081 Points
5 years ago
Let f(x)= x^3+px+q
Then f'(x)= 3x^2+p which is always greater than zero. This means that f is an increasing function. 
Now lim x tends to minus infinity f(x)= - infinity and lim x tends to infinity f(x)= infinity. So there is one and only one real root.

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