The given image shows the graph of a quadratic equation $y = ax^2 + bx + c$. Based on the graph,which of the following is true?

The roots $\alpha, \beta$ of the equation $x^2-6(k-1)x+4(k-2)=0$ are equal in magnitude but opposite in sign. If $\alpha > \beta$,then the product of the roots of the equation $2x^2-\alpha x+6\beta(\alpha+1)=0$ is

If the roots of the equation $ax^2 + x + b = 0$ are real,then the roots of the equation $x^2 - 4\sqrt{ab}x + 1 = 0$ will be

If the roots of the given equation $(\cos p-1) x^2+(\cos p) x+\sin p=0$ are real,then

Let $m$ and $n$ be two integers such that $0 \leq m \leq 10$ and $0 \leq n \leq 10$. Then,the number of ordered pairs $(m, n)$ such that $x^2+m x+n=0$ has real roots is

The expression $ax^{2} + bx + c$ (where $a, b,$ and $c$ are real numbers) has the same sign as that of $a$ for all $x \in \mathbb{R}$ if: