How 9 Cheenta students ranked in top 100 in ISI and CMI Entrances?
Learn More

Existence of Real Root

The equation x^3 + 3x - 4 has exactly one real root.


Discussion: Consider the derivative of the function f(x) = x^3 + 3x - 4 = 0 . It is 3x^2 + 3 . Note that the derivative is strictly positive ( positive times square + positive is always positive). Hence it crosses the x axis exactly once (it does cross once for large negative number will make it negative and large positive number makes it positive, hence by intermediate value property theorem it is at least once 0 in between ).

Knowledge Partner

Cheenta is a knowledge partner of Aditya Birla Education Academy

Cheenta Academy

Aditya Birla Education Academy

Aditya Birla Education Academy

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.