Quadratic Equation

The equation $\sqrt{3x^{2}+x+5}=x-3$, where $x$is real, has

Let $\alpha$ and $\beta$ be the roots of the quadratic equation $x^2-2bx+c^2=0$ where $b$, $c$ are positive real numbers. Let $A$ be the arithmetic mean of $\alpha$ and $\beta$; and $G$ be the geometric mean of $\alpha$…

If one root of the equation $x^2 - kx + k = 0$ exceeds the other by $2\sqrt{3}$, then which one of the following is a value of $k$?

The equation $x^2-4 x+29=0$ has one root $2+5 i$. What is the other root? $(i=\sqrt{-1})$

Let $f(x)=a x^2+b x+c$ such that $f(1)=f(-1)$ and $a, b, c$ are in Arithmetic Progression. What is the value of $b$ ?

If the sum of the roots of a quadratic equation is 3 and the product is 2 , then the equation is

What is the solution set for the equation $x^4-26 x^2+25=0$ ?

If one root of the equation $a x^2+b x+c=0, a \neq 0$ is reciprocal of the other root, then which one of the following is orrect?

Match the following

Let $f(x)=x^2+a x+b$, where $a, b \in R$. If $f(x)=0$ has all its roots imaginary, then the roots of $f(x)+f^{\prime}(x)+f^{\prime \prime}(x)=0$ are

$\left{x\in\,\mathbb{R}:\frac{\sqrt{6+x-x^{2}}}{2x+5}\geq\,\frac{\sqrt{6+x-x^{2}}}{x+4}\right}=$

Let $\alpha$ and $\beta$ be the roots of the quadratic equation $a x^2+b x+c=0$. Observe the lists given below The correct match of List-I from List-II is (i) (ii) (iii) (iv)