J P Mohindru and Bharat Mohindru Solutions for Chapter: Quadratic Equations, Exercise 16: CHAPTER TEST

Write the sum of real roots of the equation $x^2+5\left|x\right|-6=0$.

Write the condition to be satisfied for which the equation $a{x}^2+2bx+c=0$ and $b{x}^2-2\sqrt{ac}x+b=0$ has equal roots.

Solve $\frac{1}{x-3}-\frac{1}{x+5}=\frac{1}{6}, x\ne -3, 5$.

Solve $\frac{x-1}{x-2}-\frac{x-3}{x-4}=3\frac{1}{3}, x\ne 2, 4$.

Note: The question given in the textbook seems to be wrong. The correct question should be as below:

Solve $\frac{x-1}{x-2}+\frac{x-3}{x-4}=3\frac{1}{3}, x\ne 2, 4$.

Find two numbers whose sum is $27$ and product is $182$.

A motorboat whose speed is $18 \mathrm{km}/\mathrm{h}$ in still water, takes $1 \mathrm{hour}$ more to go $24 \mathrm{km}$ upstream than to return downstream to the same spot. If the speed of the stream is $y \mathrm{km}/\mathrm{h}$, then find the value of $y$.

The altitude of a right-triangle is $7 \mathrm{cm}$ less than its base. If the hypotenuse is $13 \mathrm{cm}$, find the other two sides.

A train travels $360 \mathrm{km}$ at a uniform speed. If the speed had been $5 \mathrm{km}/\mathrm{h}$ more, it would have taken $1 \mathrm{hour}$ less for the same journey. If the original speed of the train is $y \mathrm{km}/\mathrm{h}$, then the value of $y$ is