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Quadratic Equations

Short Answer Type

61. Represent the following situation in the form of a quadratic equation:
The sum of the ages of a son and his father (in years) is 35 and the product of their ages is 150.

130 Views

62. Represent the following situation in the form of a quadratic equation:
The product of Aditya’s age in years, five years ago with his age in years 9 years later is 15.

110 Views

63. Find the discriminant of the following quadratic equation, and hence find the nature of its roots.
$space space 2 straight x squared minus 4 straight x plus 3 equals 0$

We have,
2x² – 4x + 3 = 0
Here, a = 2, b = – 4, c = 3
Now, D = b² – 4ac
= (–4)² – 4(2) (3) = 16 – 24 = –8
Since, D < 0
Therefore, the given quadratic equation has no real roots.

115 Views

64. Find the discriminant of the following quadratic equation, and hence find the nature of its roots.

3 straight x squared minus 2 straight x plus 1 third equals 0

155 Views

65. Find the discriminant of the following quadratic equation, and hence find the nature of its roots.

2 straight x squared minus 3 straight x plus 5 equals 0

94 Views

66. Find the discriminant of the following quadratic equation, and hence find the nature of its roots.

3 straight x squared minus 4 square root of 3 straight x plus 4 equals 0

102 Views

67. Find the discriminant of the following quadratic equation, and hence find the nature of its roots.

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102 Views

68. Find the discriminant of the following quadratic equation, and hence find the nature of its roots.

2 square root of 3 straight y squared minus 14 straight y plus 4 square root of 3 equals 0

102 Views

69. Find the discriminant of the following quadratic equation, and hence find the nature of its roots.

space space 4 straight y squared minus 2 straight y plus 1 fourth equals 0

146 Views

70. Find the discriminant of the following quadratic equation, and hence find the nature of its roots.

2 straight x squared plus 5 square root of 2 straight x plus 6 equals 0

98 Views