Quadratic Equations

The product of two consecutive positive integers is $30$. This can be expressed algebraically as

In a flight of $600 \mathrm{km}$, an aircraft was slowed due to bad weather. Its average speed for the trip was reduced by $200 \mathrm{km}/\mathrm{hr}$ and time of flight increased by $30$ minutes. Find the original duration of flight.

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

One side of a triangle is $2 \mathrm{cm}$ shorter than the hypotenuse and $7 \mathrm{cm}$ longer than the third side. Find the side lenghts of the triangle.

When the square of a number is decreased by $1$, the result is $4$ times the original number. Find the number.

Find a quadratic equation with roots $\frac{3}{4} \mathrm{and} -5$ with only integer coefficients.

Write a quadratic equation in standard form that has solutions $-2 \mathrm{and} 4$

Write a quadratic equation in standard form whose only solution is $x=-\frac{3}{4}$.

Write a quadratic equation in standard form whose only solution is $x=-2$.

Solve for the variable $-3c^2=-6c+3$, if possible, using the quadratic formula, leaving your answers exact. Remember to set the equation equal to $0$, when necessary.

If the expression $x^2-20x-a$ is a perfect square, then the value of $a$ is

Solve $5x^2-4x-12=0$ by Sridhara Acharya's method.

Check whether the equation $\left(2x-1\right)\left(x-3\right)=\left(x+5\right)\left(x-1\right)$ is quadratic or not?

Check whether the equation $3y^2=192$ is quadratic or not?

A piece of wire $8 \mathrm{m}$. in length, cut into two pieces, and each piece is bent into a square. Where should the cut in the wire be made if the sum of the areas of these square is to be $2 {\mathrm{m}}^2$.

Write three polynomials that have no zeroes for $x$ that are real numbers.

Which of the following is not a quadratic equation? 

If $460$ is divided by a natural number, quotient is $6$ more than five times the divisor and remainder is $1$. Find quotient and divisor.

Pintu takes $6$ days more than those of Nishu to complete certain work. If they work together, they finish it in $4$ days. How many days would it take to complete the work if they work alone.

The difference between squares of two numbers is $120$. The square of smaller number is twice the greater number. Find the numbers.