Recent questions tagged cubic-equations

3 votes
1 answer
1
The condition that ensures that the roots of the equation $x^3-px^2+qx-r=0$ are in $H.P.$ is$r^2-9pqr+q^3=0$$27r^2-9pqr+3q^3=0$$3r^3-27pqr-9q^3=0$$27r^2-9pqr+2q^3=0$
0 votes
1 answer
2
Suppose all the roots of the equation $x^3 +bx-2017=0$ (where $b$ is a real number) are real. Prove that exactly one root is positive.
0 votes
0 answers
3
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