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Quadratic Equations

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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