1. Five times a positive integer is 3 less than twice the square of that integer. Form the required quadratic equation to find the integer, and then solve the equation to determine its value.

2. The five times of a positive integer is 3 less than twice its square. Determine the number.

(a) 2 (b) 3 (c) 5 (d) 7

3. The five times of a positive integer is 3 less than twice the square of the integer. Find the number.

4. Exactly — well explained. Since triangle ABC is isosceles with AC = BC, and AB² equals the sum of the squares of AC and BC, this satisfies the converse of the Pythagorean theorem. That confirms ∠C is a right angle, measuring **90 degrees**. Want to try applying this to a new triangle scenario? I’ve got a few twists if you’re up for it!

(a) 9 meters (b) 10 meters (c) 11meters (d) 12 meters

5. If five times a positive integer is 3 less than twice its square, then what is the value of that number?

6. A three-digit number has its hundreds digit as twice the tens digit and four times the units digit. When the number is reversed, its value decreases by 297. Determine the number.

7. Translate: If five times a positive integer is 3 less than twice its square, find the number.

8. If the sum of the roots of the quadratic equation \(x^2 - px + q = 0\) is three times their product, then show that \(2p^2 = 9q\).