- #1
lmamaths
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Hi,
A cubic equation has at least one real root.
Can someone help me to prove this?
Thx!
LMA
A cubic equation has at least one real root.
Can someone help me to prove this?
Thx!
LMA
A cubic equation is a polynomial equation of the form ax^3 + bx^2 + cx + d = 0, where a, b, c, and d are constants and x is the variable.
This can be determined by the fundamental theorem of algebra, which states that a polynomial equation of degree n has exactly n complex roots. Since a cubic equation has a degree of 3, it must have at least one real root.
Sure, one example is x^3 - 2x + 5 = 0. This equation has a real root of approximately 1.38.
One way to prove this is by using the intermediate value theorem, which states that if a continuous function has different signs at two points, there must be at least one root between those two points. The cubic equation can be represented as a continuous function, and by finding two points with different signs, we can prove that there is at least one real root.
Yes, if all three roots of the cubic equation are complex numbers, then there will be no real roots. This can happen if the discriminant, b^2 - 4ac, is negative.