Is there any value of $k$ for which the equation $x^2+2x+\left(k^2+1\right)=0$ has real roots?

Write the value of $k$ for which $x^2+4x+k$ is a perfect square.

Find the value of $k$ for which $x^2-kx+4=0$ has equal roots.

Show that $x=-2$ is a solution of the equation $3x^2+13x+14=0$

Show that $x=-3$ is a solution of the equation $x^2+6x+9=0$.

Write the sum of real roots of the equation $x^2+\left|x\right|-6=0$

If $2+\sqrt{3}$ is a quadratic equation with rational coefficients, write its other root.

Note: The question given in the textbook seems to be wrong. The correct question should be as below:

If $2+\sqrt{3}$ is a root of quadratic equation with rational coefficients, write its other root.

Write a quadratic equation, sum of whose roots is $2\sqrt{3}$ and their product is $3$.

Write the condition to be satisfied for which equations $a{x}^2+2bx+c=0$ and $b{x}^2-2\sqrt{ac}x+b=0$ have equal roots.