M L Aggarwal Solutions for Chapter: Quadratic Equations, Exercise 7: CHAPTER TEST

An aeroplane flying with a wind of $30 \mathrm{km}/\mathrm{h}$ takes $40$ minutes less to fly $3600 \mathrm{km}$ than it would have taken to fly against the same wind. Find the plane's speed in $\mathrm{km}/\mathrm{h}$ flying in still air.

Two pipes running together can fill a tank in $11\frac{1}{9}$ minutes. If one pipe takes five minutes more than other to fill the tank, find the times taken by each pipe to fill the tank.

If the sum of the roots of the equation $x^2-px+q=0$ is $m$ times their difference, then prove that $p^2(m^2-1)=4m^{2}q$.

If the roots of the equation $(x-a)(x-b)-k=0$ are $c \& d$, then prove that the roots of the equation $(x-c)(x-d)+k=0$ are $a \& b$.

Determine the values of $a$ for which the equation $x^2-2(a+1)x+4=0$ has real and distinct roots.

Determine the values of $a$ for which the equation $x^2-2(a+1)x+4=0$ has equal roots.

Determine the values of $m$ for which the equation $x^2-2mx+8m-15=0$ has equal roots.

Determine the values of $m$ for which the equation $x^2-2mx+8m-15=0$ has both roots positive.