If $1-i$ is a root of the equation $x^2+ax+b=0$ where $a$ and $b$ are real numbers,then $b$ is equal to

Solve the equation $27 x^{2}-10 x+1=0$.

If $\alpha$ and $\beta$ are two complex roots of the equation $6x^6-25x^5+31x^4-31x^2+25x-6=0$,then $\alpha+\beta=$

The product of the roots of the equation $9x^{2}-18|x|+5=0$ is

Let $a, b, c$ be real numbers with $a \ne 0$. If $\alpha$ is a root of $a^2x^2 + bx + c = 0$,$\beta$ is a root of $a^2x^2 - bx - c = 0$,and $0 < \alpha < \beta$,then the equation $a^2x^2 + 2bx + 2c = 0$ has a root $\gamma$ that always satisfies:

The number of real values of $a$ satisfying the equation $a^2 - 2a\sin x + 1 = 0$ is