Quadratic Equat...

Find the roots of the following quadratic equation (if they exist) by the method of completing the square.
$$x^2 \, - \, (\sqrt{2} \, + \, 1)  \, x \, + \, \sqrt{2} \, = \, 0$$

Using the identity $$\left( {x + a} \right)\left( {x + b} \right),$$ the value of $$\left( {2a - 1} \right)\left( {2a + 2} \right)$$

Which of the following statements is TRUE/CORRECT about Quadratic Equations? A quadratic equation is _____

Which of the following methods is used to derive the Standard Quadratic Formula for the Quadratic Equation $$ax^2+bx+c=0$$?

If ($$\alpha $$, $$\beta $$) are the roots of $$a{x^2} + bx + c = 0$$ ,$$\left( {a \ne 0} \right)$$ and ($$\alpha  + \delta $$ , $$\beta  + \delta $$) are the roots of $$A{x^2} + Bx + C = 0,\ (A \ne  0)$$ for some constant $$\delta $$, then the value of  $$\delta$$  is

For $$a \le 0$$, the roots of the equation $${x^2} - 2a\left| {x - a} \right| - 3{a^2} = 0$$ is

The value of $$'a'$$ for which the quadratic equation $$2{x^2} - x\left( {{a^2} + 8a - 1} \right) + {a^2} - 4a = 0$$ has roots opposite signs, lie in the interval 

Find the roots of the equation $$5x^{2} -6x-2 = 0$$ by the method of completing the square.

The roots of the given equation $$\left( {p - q} \right){x^2} + \left( {q - r} \right)x + \left( {r - p} \right) = 0$$  are 

Two water taps together can fill a tank in $$3\dfrac {1}{13}$$ hours. The tap of longer diameter takes $$3$$ hours less then smaller one to fill the bank separately. Find the time(hrs) in which tap of smaller diameter can separately fill the tank.