Practice the questions given in the worksheet on formation of quadratic equation in one variable. We need to form a quadratic equation in one variable from a mathematical problem.
1. Which of the following is not a quadratic equation?
(a) y = x
(b) y = 2x^2
(c) y = 5x^2 + 2x  7
(d) A = s^2
(e) A = πr^2
2. Area of a rectangular play ground, having length 8 meters more than its breadth, is 48 square meters.
3. 42 is divided into two parts, such that one part is the square of the other. Form the equation.
4. Identify whether the following are quadratic expression or not:
(a) 5x  3 = 0
(b) z(z  1) = 3
(c) (x + 5)(x + 6)  x(x  7) = 25
(d) x  7 + 5/x = 35
(e) (x  6)^2 = x^2  2x + 8
5. The owner of a garden, where there are some coconut trees; produce in each coconut tree is one more than the total number of coconut trees in the garden. If the total number of coconut is 342, then form the equation.
6. Product of two consecutive positive odd integers is 143. Form the equation.
7. Sum of the squares of two consecutive integers is 313. Form the equation.
8. Ron bought some packets of chocolates for $ 80. He got 4 packets more at the same price, the price of each packet of chocolates have been less by $1.
9. The length of the diagonal of a rectangular park is 15 m and one of its sides is longer than another by 3 m.
10. The speed of current is 4 km/hour. A boat takes 3 hours to go 18 km downstream and return 6 km upstream.
11. Two stations Maharashtra and Thane are 300 km apart. A bus goes from the station Maharashtra toThane at a uniform speed. If the speed of the bus been 5 km/hour more it would have taken 2 hours less to travel the same distance.
12. A path of uniform width surrounds a rectangular garden of length 45 m and breadth 40 m; the area of the path is 450 sqm .
13. In a two digits number, the digit in the unit’s place more than that in the ten’s place by 6. The product of the digits is less than the number by 12.
14. A electronic dealer bought a calculator and sold it for $ 336. He gained as much in percentage as was his cost price.
15. When the speed of the water is 2 km/hour, a swimmer takes 5 hours to go 14 kilometers downstream and to return.
Answers for the worksheet on formation of quadratic equation in one variable are given below.
Answers:
1. (a)
2. x(x + 8)= 48
3. x^2 = 42 –x or (42 – x)^2 = x
4. (a) No this is not a quadratic equation.
(b) Yes it is a quadratic equation.
(c) No this is not a quadratic equation.
(d) Yes it is a quadratic equation.
(e) No this is not a quadratic equation.
5. x(x + 1) = 342
6. x (x + 2) = 143 or (x – 2)x = 143
7. x^2 + (x + 1)^2 = 313 or, (x – 1)^2 + x^2 = 313
8. 80/x = 80/(x + 4) + 1
9. x^2 + (x + 3)^2 = 15^2 or, (x – 3)^2 + x^2 = 15^2
10. 18/(x + 4) + 6/(x – 4) = 3
11. 300/x – 300/(x+ 5) = 2
12. (45 + 2x)(40 + 2x) – 45 × 40 = 450
13. x(x + 6) = (10x + x + 6) – 12 or, (x – 6) x = 10(x – 6) + x  12
14. 336 – x = x^2/100
15. 14/(x + 2) + 14/(x – 2) = 5
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