Let $a, b, c$ be non-zero real roots of the equation $x^3+a x^2+b x+c=0$. Then,
Let $a, b, c$ be non-zero real roots of the equation $x^3+a x^2+b x+c=0$. Then,
- [KVPY 2020]
- A
There are infinitely many such triples $a, b, c$
- B
There is exactly one such triple $a, b, c$
- C
There are exactly two such triples a, $b, c$
- D
There are exactly three such triples a, $b, c$
Similar Questions
If the graph of $y = ax^3 + bx^2 + cx + d$ is symmetric about the line $x = k$ then
If the graph of $y = ax^3 + bx^2 + cx + d$ is symmetric about the line $x = k$ then
If the expression $\left( {mx - 1 + \frac{1}{x}} \right)$ is always non-negative, then the minimum value of m must be
If the expression $\left( {mx - 1 + \frac{1}{x}} \right)$ is always non-negative, then the minimum value of m must be
If $\alpha ,\beta ,\gamma$ are the roots of $x^3 - x - 2 = 0$, then the value of $\alpha^5 + \beta^5 + \gamma^5$ is-
If $\alpha ,\beta ,\gamma$ are the roots of $x^3 - x - 2 = 0$, then the value of $\alpha^5 + \beta^5 + \gamma^5$ is-
The sum of the roots of the equation $x+1-2 \log _{2}\left(3+2^{x}\right)+2 \log _{4}\left(10-2^{-x}\right)=0$, is :
The sum of the roots of the equation $x+1-2 \log _{2}\left(3+2^{x}\right)+2 \log _{4}\left(10-2^{-x}\right)=0$, is :
- [JEE MAIN 2021]
If $\alpha ,\beta $are the roots of ${x^2} - ax + b = 0$ and if ${\alpha ^n} + {\beta ^n} = {V_n}$, then
If $\alpha ,\beta $are the roots of ${x^2} - ax + b = 0$ and if ${\alpha ^n} + {\beta ^n} = {V_n}$, then