Algebra

# Quadratic Equations - Word Problems

The equation $$2x^2 - 62x + k = 0$$ has two real roots, one of which is 1 more than twice the other. Find the value of $$k$$.

The product of 2 consecutive positive odd integers is 675. What is the sum of these 2 integers?

The height of a triangle is 7 less than its base. If the area of the triangle is 225, what is its height?

Two taps $$A$$ and $$B$$ can fill a swimming pool in 5 hours. If turned on alone, it takes tap A 3 hours less than tap B to fill the same pool. How many hours does it take tap A to fill the pool?

In 20 years, Frank will be half the square of the age he was 4 years ago. How old is Frank now?

A ball is rolling down the slope. It was initially released with a speed of 2 m/s , and it speeds up with a constant acceleration of 4 m/s$$^2$$. The distance in meters that this object travels is $$t$$ seconds is given by

$d = 2 t^2 + 2 t .$

How long will it take the object to travel 12 meters?

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