Given below are two statements:

Statement (I): (x² + 3x + 1) = (x - 2)² is not a quadratic equation.

Statement (II): The nature of roots of quadratic equations x² + 2x√3 + 3 = 0 are real and equal.

In light of the above statements, choose the most appropriate answer from the options given below.

If the roots of the equation $x^{2}-p x+54=0$ are in the ratio $2: 3$, then value of $p$ is:

If one root of the quadratic equation $ax^2+bx+c=0$ is the reciprocal of other, then which of the following is correct?

If $\sin (\alpha)$ and $\cos (\alpha)$ are the roots of the equation $a x^{2}+b x+c=0$, then $b^{2}$ is

The factors of polynomial $x^{3}-6 x^{2}+11 x-6$ are :

Let $p$ and $q$ be the roots of the quadratic equation $ax^2+bx+c=0$, $a\ne0$. If $a$, $b$ and $c$ are in arithmetic progression and $\frac{1}{p}+\frac{1}{q}=4$, then the value of $(p-q)^2$ is

Amit and Alok attempted to solve a quadratic equation. Amit made a mistake in writing down the constant term and ended up with roots $(4, 3)$. Alok made a mistake in writing down coefficient of $x$ to get roots $(3, 2)$. The correct roots of the equation are: