The number of roots of the equation $\log ( - 2x)$ $ = 2\log (x + 1)$ are
$3$
$2$
$1$
None of these
If the sum of the two roots of the equation $4{x^3} + 16{x^2} - 9x - 36 = 0$ is zero, then the roots are
Suppose $a$ is a positive real number such that $a^5-a^3+a=2$. Then,
The number of cubic polynomials $P(x)$ satisfying $P(1)=2, P(2)=4, P(3)=6, P(4)=8$ is
Let $a, b$ be non-zero real numbers. Which of the following statements about the quadratic equation $a x^2+(a+b) x+b=0$ is necessarily true?
$I$. It has at least one negative root.
$II$. It has at least one positive root.
$III$. Both its roots are real.
If $x$ is real, the expression $\frac{{x + 2}}{{2{x^2} + 3x + 6}}$ takes all value in the interval