Problem 1-4 : Solve the quadratic equation using the quadratic formula.
Problem 1 :
2x2 – 5x + 2 = 0
Problem 2 :
√2f2 - 6f + 3√2 = 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.
1. Answer :
Comparing ax2 + bx + c = 0 and 2x2 – 5x + 2 = 0, we get
a = 2, b = -5, c = 2
Quadratic Formula :
Substitute a = 2, b = -5 and c = 2.
2. Answer :
√2f2 - 6f + 3√2 = 0
From the quadratic equation above,
a = √2, b = -6, c = 3√2
Substitute the above values into the quadratic formula.
3. Answer :
3y2 - 20y - 23 = 0
From the quadratic equation above,
a = 3, b = -20, c = -23
Substitute the above values into the quadratic formula.
4. Answer :
36y2 - 12ay + (a2 - b2) = 0
From the quadratic equation above,
a = 36, b = -12a, c = a2 - b2
Substitute the above values into the quadratic formula.
5. Answer :
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
From the quadratic equation above,
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.
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
©All rights reserved. onlinemath4all.com
Oct 03, 23 12:56 AM
Oct 03, 23 12:34 AM
Oct 02, 23 11:40 PM