Bidyut Guha Thakurta and Amitava Mitra Solutions for Exercise 2: EXERCISE 1B

Only one root of the equation $k(x^2+x+1)+2=0$ will be zero, if $k=$_____.

The roots of the equation $p{x}^2+qx+r=0,(p\ne 0)$ will be equal if $p^2=qr$.

The equation whose roots are $2$ and $-3$, is $x^2-x-6=0$.

One root of the equation $2x^2+3x-2=0$ is $-2$.

Both roots of the equation $(k-1)x^2+(k+1)x=0$ will be zero, if $k=0$.

$x^2=0$ is not a quadratic equation.

$\frac{x^2}{x}=6$ is a quadratic equation.

If ${(x-\frac{1}{3})}^2=0$, then the value of ${(x+\frac{2}{3})}^2$ is $1$.