PRACTICE QUESTIONS INVOLVING QUADRATIC EQUATIONS

Problem 1 :

The product of the number and the number increased by 4 is 96. Find the two possible answers for the number.

Solution

Problem 2 :

When 24 is subtracted from the square of a number the result is five times the original number. Find the number ?                Solution

Problem 3 :

The sum of two numbers is 8 and the sum of their squares is 34. Taking one number as x form an equation in x and hence find the numbers. The numbers are 

Solution

Problem 4 :

The difference of two positive integers is 3 and the sum of their squares is 89. Taking the smaller integer as x form a quadratic equation and solve it to find the integers. The integers are,            Solution

Problem 5 :

There are two consecutive numbers such that the difference of their reciprocals is 1/240. The numbers are          Solution

Problem 6 :

The sum of two irrational numbers multiplied by the larger one is 70 and their difference is multiplied by the smaller one is 12, the two numbers are

Solution

Problem 7 :

Difference between a number and its positive square root is 12. Find the number. 

Solution

Problem 8 :

A piece of iron rod costs $60. If the rod was 2 meter shorter and each meter costs $1 more, the cost would remain unchanged. What is the length of the rod ? 

Solution

Problem 9 :

Divide 25 in two parts so that sum of their reciprocals is 1/6.         Solution

Problem 10 :

The hypotenuse of a right angled triangle is 20 cm. The difference between its other two sides is 4 cm. Find the length of the sides.            Solution

Problem 11 :

The sides of an equilateral triangle are shortened by 12 units, 13 units and 14 units respectively and a right angle triangle is formed. Find the length of each side of the equilateral triangle.       Solution

Answers :

(1)   8 or - 12

(2)   8 or – 3

(3)  3 and 5.

(4)   5 and 8

(5)  15 and 16

(6)  50 and 49

(7)  x  =  16

(8)  12 m.

(9)  25 are 10 and 15.

(10)  12 cm and 16 cm

(11)  17 units

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