Quadratic Equation

$\left(1+m^2\right)x^2+2 mcx+c^2-a^2=0$ has equal roots if ________.

What is the solution of the equation $\sqrt{\frac{x}{x+3}}-\sqrt{\frac{x+3}{x}}=-\frac{3}{2}$?

Which of the following equations has real roots$?$

If $I\pm I^2$² are the roots of $x^2+px+12=0$ and $I\pm -I^2=1$ then its roots-

If $x^2+1-2x=0,x>0$, then $x^2\left(x^2-2\right)$ ______.

If the roots of $a{x}^2+bx+c=0$ are in the ratio $\frac{p}{q}$ then the value of $\frac{b^2}{\left(ca\right)}$ is______.

If $\alpha ,\beta$ are the roots of equation $x^2-5x+6=0$ and $\alpha >\beta$ then the equation with roots $(\alpha \beta +\alpha +\beta )$ and $(\alpha \beta -\alpha -\beta )$ is

If $\alpha ,\beta$ are the roots of equation $x^2-5x+6=0$ and $\alpha >\beta$ then the equation with roots $\left({\alpha }^2+\beta \right)$ and $\left(\alpha +{\beta }^2\right)$ is

Solving equation $\sqrt{x^2-9x+18}+\sqrt{x^2+2x-15}=\sqrt{x^2-4x+3}$ following roots are obtained

If the roots of the equation $2x^2+8x-m^3=0$ are equal then value of $m$ is _____.

If sum of the roots of a quadratic equation is$7$ and  product of the roots is $12$ . Find the quadratic equation.

What will be the roots of the quadratic equation ${\mathrm{x}}^2-25\mathrm{x}+156=0?$

It is given that ${\mathrm{p}}^2$ and ${\mathrm{q}}^2$ are the roots of ${\mathrm{x}}^2 + \mathrm{ax} + \mathrm{b} = 0$, and that $\mathrm{p}$ and $\mathrm{q}$ are the roots of ${\mathrm{x}}^2 + \mathrm{cx} + \mathrm{d} = 0$. If $\mathrm{a} = -2$ and $\mathrm{p}$ and $\mathrm{q}$ are real numbers, then determine the minimum possible value of $\mathrm{c}$.

Find the values of $x$ for the given equation $3x^2 + 5x – 2 = 0$.

If roots of $x^2-4x+k=0$ are equal, then $k$ equal to:

The solution of $2x^2-5x+3=0$ is

The roots of the quadratic equation $3q^2–2q=8$ are

Equation $3x^2+1344x-42=0$ has roots $p$ and $q$ then what will be the sum of $\frac{2}{p}+\frac{2}{q}?$

Sum of the roots of a quadratic equation is $9$ less than the product of the roots. If one root is $3$ more than the other root, find the product of the roots?

Equation$x^2+5x-7=0$ has roots a and b. Equation $2x^2+px+q=0$ has roots $a+2$ and $b+2$ find $p-q$?