The number of solution$(s)$ of the equation $2^x = x^2$ is

Let $p_1(x)=x^3-2020 x^2+b_1 x+c_1$ and $p_2(x)=x^3-2021 x^2+b_2 x+c_2$ be polynomials having two common roots $\alpha$ and $\beta$. Suppose there exist polynomials $q_1(x)$ and $q_2(x)$ such that $p_1(x) q_1(x)+p_2(x) q_2(x)=x^2-3 x+2$. Then the correct identity is

Consider the cubic equation $x^3+c x^2+b x+c=0$ where $a, b, c$ are real numbers. Which of the following statements is correct?

Solution of the equation $\sqrt {x + 3 - 4\sqrt {x - 1} }  + \sqrt {x + 8 - 6\sqrt {x - 1} }  = 1$ is

The roots of $|x - 2{|^2} + |x - 2| - 6 = 0$are

A real root of the equation ${\log _4}\{ {\log _2}(\sqrt {x + 8} - \sqrt x )\} = 0$ is