If $x$ is real,then the maximum and minimum values of $\frac{x^2+14x+9}{x^2+2x+3}$ are respectively

Let $a_1, a_2, a_3, a_4$ be real numbers such that $a_1+a_2+a_3+a_4=0$ and $a_1^2+a_2^2+a_3^2+a_4^2=1$. Then,the smallest possible value of the expression $(a_1-a_2)^2+(a_2-a_3)^2+(a_3-a_4)^2+(a_4-a_1)^2$ lies in the interval

Two roots of the equation $ax^4 + bx^3 + cx^2 + dx + e = 0$ are positive and equal. If the product of the other two real roots is $1$,then:

The sum of all the roots of the equation $|x^2-8x+15|-2x+7=0$ is:

Let $(a-3)x^2+12x+(a+6)>0, \forall x \in R$ and $a \in (\ell, \infty)$. If $\alpha$ is the least positive integral value of $a$,then the roots of $(\alpha-3)x^2+12x+(\ell+2)=0$ are

Let the transformed equation of $2x^4-8x^3+3x^2-1=0$ such that the term containing the cubic power of $x$ is absent be $2x^4+bx^2+cx+d=0$. Then $b=$