Quadratic Integer Problems

The sum of a number and its square is 72. Find the number.

• 8 or 9

• 8 or -9

• -8 or 9

• -8 or -9

If you square 5 more than a positive number, the result is 88 more than 12 times the number. Find the number.

• 7

• -7

• 9

• -9

The sum of two numbers is 12 and the sum of their squares is 80. Find the numbers.

• 4 and 8

• 6 and 6

• 2 and 10

• 3 and 9

The length of a rectangle is 4 cm more than its width. The area of the rectangle is 96 sq. cm. Find its dimensions.

• 4 cm by 8 cm

• 6 cm by 10 cm

• 8 cm by 12 cm

• 10 cm by 14 cm

The perimeter of a rectangle is 30 cm. Its area is 54 cm² . Find the dimensions of this rectangle.

• 5 cm by 10 cm

• 6 cm by 9 cm

• 7 cm by 8 cm

• 11 cm by 4 cm

One number is 3 more than another. The sum of their squares is 149. Find the numbers.

• 4 and 7; -4 and -7

• 5 and 8; -5 and -8

• 6 and 9; -6 and -9

• 7 and 10, -7 and -10

The product of two consecutive positive numbers is 132. Find the numbers.

• 11 and 12

• 13 and 14

• 15 and 16

• 17 and 18

The sum of the squares of two consecutive positive even integers is 340. Find the integers.

• 10 and 12

• 12 and 14

• 14 and 16

• 16 and 18

The length of a rectangle is 1 m longer than 3 times its width. The area is 80 m² . Find the dimensions of this rectangle.

• 4m by 13m

• 5m by 16m

• 6m by 19m

• 7m by 22m

The length of a rectangle is 3 times its width. If the width is increased by 2 cm and the length is increased by 4 cm, its area will be doubled. Find the original dimensions of the rectangle.

• 7cm by 21cm

• 6cm by 18cm

• 5cm by 15cm

• 4cm by 12cm