Find the condition that in the equations $\displaystyle ax^{3}+bx+c=0$ and $dx^{2}+b'x+c'=0$
Step $1: x^{2} - 3x^{2}y^{2} + x^{2}y^{2} - 2x^{2} - 3y^{2} + 12x^{2}y^{2}$
Step $2 : (x^{2} - 2x^{2}) + (-3x^{2}y^{2} + x^{2}y^{2} + 12x^{2}y^{2}) - 3y^{2}$
Step $3 : (-x^{2} + 10x^{2}y^{2} - 3y^{2})$
$x^{2} (1 - 3y^{2}) + (xy^{2} - 2x) - 3y(y - 4x^{2}y)$?
If the graph of a quadratic polynomial $ax^2+bx+c$ touches the X-axis at two points (as shown above), which of the following statements is correct?
$3\sin^{2}x-7\sin x+2=0$
in the interval $[0, 5\pi]$ is:-