If the graph of $y = ax^3 + bx^2 + cx + d$ is symmetric about the line $x = k$ then
$k=c$
$k = -\frac{c}{b}$
$a + \frac{c}{{2b}} + k = 0$
none of these
Let $a$ , $b$ , $c$ are roots of equation $x^3 + 8x + 1 = 0$ ,then the value of
$\frac{{bc}}{{(8b + 1)(8c + 1)}} + \frac{{ac}}{{(8a + 1)(8c + 1)}} + \frac{{ab}}{{(8a + 1)(8b + 1)}}$ is equal to
If $\alpha , \beta$ and $\gamma$ are the roots of ${x^3} + 8 = 0$, then the equation whose roots are ${\alpha ^2},{\beta ^2}$ and ${\gamma ^2}$ is
The solutions of the quadratic equation ${(3|x| - 3)^2} = |x| + 7$ which belongs to the domain of definition of the function $y = \sqrt {x(x - 3)} $ are given by
The number of distinct real roots of $x^4-4 x^3+12 x^2+x-1=0$ 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 :