SOLVING PROBLEMS INVOLVING QUADRATIC EQUATIONS || GRADE 9 MATHEMATICS Q1

Summary

This video tutorial explains how to solve quadratic equations through real-world examples. The instructor starts by solving a problem involving the dimensions of a rectangular table, using area and perimeter calculations. Next, another problem explores finding two numbers based on their sum and sum of squares, while factoring quadratic equations. Finally, the video covers how to apply the Pythagorean theorem to determine the sides of an inclined ramp. The video emphasizes step-by-step solutions and checks for accuracy, making it a useful guide for math learners. Viewers are encouraged to like, subscribe, and stay updated for more tutorials.

Takeaways

• 📘 The video tutorial focuses on solving problems involving quadratic equations.
• 📏 The first problem involves finding the dimensions of a rectangular table with a given area and perimeter.
• 🔢 The area of the rectangle is given as 27 square feet, and the perimeter as 24 feet.
• 📐 The formula for the area of a rectangle is length times width, and for the perimeter, it's twice the length plus twice the width.
• 🧮 The sum of the roots of the quadratic equation is found to be 12, and the product of the roots is 27.
• 🔍 The quadratic equation is solved by factoring, yielding the dimensions of the table as 3 feet by 9 feet.
• 📐 The solution is verified by checking that the area and perimeter calculations match the given values.
• 🔢 The second problem involves finding two numbers given their sum and the sum of their squares.
• 📘 The third problem is about finding the lengths of the sides of a ramp, given the relationship between the rise, run, and length of the ramp.
• 📐 The Pythagorean theorem is used to set up the equation for the ramp problem, with the hypotenuse being the length of the ramp.
• 🔍 The ramp problem's quadratic equation is solved, revealing the rise to be 5 meters, the run 12 meters, and the length 13 meters.

Q & A

What is the area of the rectangular table mentioned in the problem?

The area of the rectangular table is 27 square feet.

What is the formula used to calculate the perimeter of a rectangle?

The perimeter of a rectangle is calculated as the sum of twice its length and twice its width (P = 2L + 2W).

How are the length and width of the table related to its perimeter?

The sum of the length and width is equal to 12, based on the given perimeter of 24 feet.

What quadratic equation is formed from the sum and product of the length and width of the table?

The quadratic equation formed is x² - 12x + 27 = 0, where x represents the dimensions of the table.

What are the dimensions of the rectangular table?

The dimensions of the table are 3 feet for the width and 9 feet for the length.

How does the solution verify that the calculated dimensions are correct?

The solution checks the area (3 × 9 = 27 square feet) and the perimeter (2(3) + 2(9) = 24 feet), confirming the dimensions are correct.

What is the next problem involving the sum and squares of two numbers?

The problem involves finding two numbers whose sum is 19 and whose sum of squares is 193.

What are the two numbers found from the quadratic equation x² - 19x + 84 = 0?

The two numbers are 7 and 12.

What is the final problem in the video involving the sides of a ramp?

The problem involves finding the three sides of a ramp where the ramp is 8 meters longer than the rise, and the run is 7 meters longer than the rise.

What are the dimensions of the ramp based on the solution using the Pythagorean theorem?

The dimensions are: rise = 5 meters, run = 12 meters, and ramp length (hypotenuse) = 13 meters.