QUADRATIC EQUATIONS AND INEQUATIONS (CDS)

Total Questions: 67

31. Solve the following equation [2016 (II) Evening Shift]

Correct Answer: (d) 15
Solution:



32. In the quadratic equation x² + ax + b = 0, a and b can take any value from the set {1, 2, 3, 4}. How many pairs of values of a and b are possible in order that the quadratic equation has real roots? [2016 (II) Evening Shift]

Correct Answer: (b) 7
Solution:For real roots, B²- 4AC ≥ 0


33. The sum of the squares of two positive integers is 208. If the square of the larger number is 18 times the smaller number, then what is the difference of the larger and smaller numbers? [2016 (II) Evening Shift]

Correct Answer: (c) 4
Solution:Let two positive integers be x and y.

34. If α and β are the two zeroes of the polynomial 25x² - 15x + 2, then what is a quadratic polynomial whose zeroes are (2α)⁻¹ and (2β)⁻¹ ? [2016 (II) Evening Shift]

Correct Answer: (b) 8x² - 30x + 25
Solution:Let 25x² - 15x + 2,



35. If p and q are the roots of x² + px + q = 0, then which one of the following is correct? [2016 (II) Evening Shift]

Correct Answer: (b) p = 1only
Solution:We have, p and q are the roots of equation

36. If 2p + 3q = 12 and 4p² + 4pq - 3q² = 126, then what is the value of p + 2q ? [2016 (II) Evening Shift]

Correct Answer: (d) 99/16
Solution:Given, 2p + 3q = 12 ... (i)

37. If a and b are negative real numbers and c is a positive real number, then which of the following is/are correct? [2016 (I) Morning Shift ]

1. a - b < a - c
2. If a < b then a/c < b/c
3. 1/b < 1/c

Select the correct answer using the codes given below.

Correct Answer: (d) 2 and 3
Solution:

38. Under what condition on p and q, one of the roots of the equation x² + px + q = 0, is the square of the other? [2016 (I) Morning Shift ]

Correct Answer: (c) p³ + q + q² = 3pq
Solution:Let α and α² be the roots of equation x² + px + q = 0.

39. Solve the following equation [2016 (I) Morning Shift ]

Correct Answer: (d)
Solution:

40. Which of the points P (5, 1), Q (3, 2) and R (1, 1) lie in the solution of the system of inequations x + y ≤ 4 and x - y ≥ 2 ? [2016 (I) Morning Shift ]

Correct Answer: (c) P and Q
Solution:Given points are P(5,- 1) Q(3, - 2) and R(1, 1)