The number of real solutions of the equation $x(x^2+3|x|+5|x-1|+6|x-2|)=0$ is

If the values of $k$ for which the equation $x^2+2(k+2)x+6k+7=0$ has equal roots are $k_1$ and $k_2$,then $k_1^2+k_2^2=$

The roots of the equation $(x-a)(x-a-1)+(x-a-1)(x-a-2)+(x-a)(x-a-2)=0$ for $a \in R$ are always:

Let $A, G$ and $H$ be the arithmetic mean,geometric mean and harmonic mean,respectively,of two distinct positive real numbers. If $\alpha$ is the smallest of the two roots of the equation $A(G-H) x^2 + G(H-A) x + H(A-G) = 0$,then:

If the equation $x^4 - 4x^3 + ax^2 + bx + 1 = 0$ has four real roots $\alpha, \beta, \gamma, \delta$,then the values of $a$ and $b$ are:

If $a, b, c, d$ are real numbers such that $a < b < c < d$,then the roots of the equation $(x-a)(x-c)+2(x-b)(x-d)=0$ are