Quadratic Equation

Roots of the equation $x^2+b x-c=0(b, c\gt0)$ are

Rational roots of the equation $2 x^4+x^3-11 x^2+$ $x+2=0$ are

If $\tan 15^{\circ}$ and $\tan 30^{\circ}$ are the roots of the equation $x^2+p x+q=0$, then $p q=$

Solve $\sqrt{5} x^2+x+\sqrt{5}=0$

If one root of the equation $x^2+p x+12=0$ is 4, while the equation $x^2+p x+q=0$. has equal roots, then the value of ' $q$ ' is

Solution of $2^x+2^{|x|} \geq 2 \sqrt{2}$ is

The range of the function $f(x)=\sqrt{3 x^2-4 x+5}$ is

The roots of the given equation $(p-q) x^2+(q-r) x+(r-p)=0$ are :

Let $a, b$ be the solutions of $x^2+p x+1=0$ and $c, d$ be the solution of $x^2+q x+1=0$. If $(a-c)(b-c)$ and $(a+d)(b+d)$ are the solution of $x^2+a x+\beta=0$, then $\beta$ is equal to

If $\alpha$ be a root of the equation $4 x^2+2 x-1=0$, then the other root of the equation is

Find the value of $a$ such that the sum of the squares of the roots of the equation $x^{2}-(a-2) x-(a+1)=0$ is least?

The number of real solutions of the equation $(x-1)^{2}+(x-2)^{2}+(x-3)^{2}=0$ is