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

ajay , 7 Years ago
Grade 10
anser 1 Answers
Arun
 
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.
 
Regards
Arun
Last Activity: 7 Years ago
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