Problem 1 :

2x2 – 5x + 2 = 0

Problem 2 :

2f2 - 6f + 32 = 0

Problem 3 :

3y2 - 20y - 23 = 0

Problem 4 :

36y2 - 12ay + (a2 - b2) = 0

Problem 5 :

A ball rolls down a slope and travels a distance d = t2 - 0.75t feet in t seconds. Find the time when the distance traveled by the ball is 11.25 feet. Comparing ax2 + bx + c = 0 and 2x2 – 5x + 2 = 0, we get

a = 2, b = -5, c = 2

Substitute a = 2, b = -5 and c = 2.

2f2 - 6f + 32 = 0

a = √2, b = -6, c = 3√2

Substitute the above values into the quadratic formula.

3y2 - 20y - 23 = 0

a = 3, b = -20, c = -23

Substitute the above values into the quadratic formula.

36y2 - 12ay + (a2 - b2) = 0

a = 36, b = -12a, c = a2 - b2

Substitute the above values into the quadratic formula.

d = t2 - 0.75t

We have to find the time when the distance traveled by the ball is 11.25 feet.

Substitute d = 11.25 into the above equation and solve for t.

11.25 = t2 - 0.75t

t2 - 0.75t - 11.25 = 0

Multiply both sides by 100 to get rid of the decimal point.

100(t2 - 0.75t - 11.25) = 100(0)

100t2 - 75t - 1125 = 0

Divide both sides by 25.

4t2 - 3t - 45 = 0

a = 4, b = -3, c = -45

Substitute the above values into the quadratic formula.

t = 3.75  or  -3

Time can never be a negative value. So, t = -3 can be rejected.

Therefore,

t = 3.75 seconds

The ball takes 3.75 seconds to travel a distance of 11.25 feet.

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