Quadratic Equations

If the roots of the equation${\mathrm{x}}^2+2(3\mathrm{a}+5)\mathrm{x}+2(9{\mathrm{a}}^2+25)=0$ are rational, then the value of $\mathrm{a}$ is _____.

If x is real, the minimum value of 4x ² + 4 x+ 9 is

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

Quadratic equation corresponding to the roots $2+\sqrt{5} \& 2-\sqrt{5}$ is ______.

If $\left(–4\right)$ is one root of the equation $x^2+px-4=0$ and the equation $x^2+px+q=0$ has equal roots then the value of $p$ and $q$ are respectively.

Find the maximum value of $\frac{2x^2+3x+4}{x^2+x+3}?$

Which of the following equations has real roots$?$

The roots of equation $y^3+y^2-y-1=0$ are

Which of the quadratic equations has imaginary roots?

$$\begin{gathered} A.) x^2+1=0 \\ B.) x^2-7x+12=0 \\ C.) x^2+9=0 \\ D.) x^2-11x+30=0 \end{gathered}$$

Which one of the quadratic equations has real and unequal roots?

$$\begin{gathered} A.) x^2-12x+36=0 \\ B.) x^2-18x+81=0 \\ C.) x^2-20x+99=0 \\ D.) x^2-2x+1=0 \end{gathered}$$

Which one of the quadratic equations has real and equal roots?

$$\begin{gathered} A.) x^2-8x+16=0 \\ B.) x^2-7x+12=0 \\ C.) x^2-9x+20=0 \\ D.) x^2-11x+30=0 \end{gathered}$$

Match the List $\mathrm{I}$ and List $\mathrm{II}$ and select the correct answer using code:

Match the List $\mathrm{I}$ and List $\mathrm{II}$ and select the correct answer using code:

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

If $P={(7P^3+8)}^{\frac{1}{6}}$   then how many integral values of $P$ exists?

What is the minimum value of the ratio of the sum of the cubes of the roots of the equation $x^2-ax+\left(2a-4\right)=0$ to $a,$ given that $a$ is real?

Find the roots of the given quadratic equation:

$x^2-6x+5=0$

Find the roots of the given quadratic equation:

$x^2-14x+24=0$