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What is the condition for the cubic equation ax^3 +bx^2 +cx+d = 0 to have real roots? (not Graphically but in terms of the coefficients a,b,c,d, ie., like we have for a quadratic eqn. that D>0)

What is the condition for the cubic equation ax^3 +bx^2 +cx+d = 0


to have real roots? (not Graphically but in terms of the coefficients a,b,c,d, ie., like we have for a quadratic eqn. that D>0) 

Grade:upto college level

1 Answers

Pratik Tibrewal
askIITians Faculty 37 Points
7 years ago
as such there is no single condition which we can use to solve the cubic.
But we can approach it in some algebraic steps:
1. differentiate, and the quadratic obtained should have D>0
2. Let's say the two roots of the quadratic obtained above is x1,x2.

Then if P(x1). P(x2) < = 0 then it has 3 real roots.

Thanks and Regards,
Pratik Tibrewal,
askiitians faculty,
BTech IITG

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