Let $a, b, c$ be non-zero real roots of the equation $x^3+a x^2+b x+c=0$. Then,
There are infinitely many such triples $a, b, c$
There is exactly one such triple $a, b, c$
There are exactly two such triples a, $b, c$
There are exactly three such triples a, $b, c$
Sum of the solutions of the equation $\left[ {{x^2}} \right] - 2x + 1 = 0$ is (where $[.]$ denotes greatest integer function)
The two roots of an equation ${x^3} - 9{x^2} + 14x + 24 = 0$ are in the ratio $3 : 2$. The roots will be
The polynomial equation $x^3-3 a x^2+\left(27 a^2+9\right) x+2016=0$ has
The locus of the point $P=(a, b)$ where $a, b$ are real numbers such that the roots of $x^3+a x^2+b x+a=0$ are in arithmetic progression is
If $x$ be real, then the maximum value of $5 + 4x - 4{x^2}$ will be equal to