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Let the present age of Aditya’s be x years. Aditya’s age five years ago = (x – 5) years Aditya’s age nine years later = (x + 9) years According to question, (x – 5) (x + 9) = 15 x 2 + 9x – 5x – 45 = 15 x 2 + 4x – 60 = 0 Therefore, the required representation in the form of quadratic equation be x 2 + 4x – 60 = 0.

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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.

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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.

Let the present age of Aditya’s be x years.
Aditya’s age five years ago = (x – 5) years
Aditya’s age nine years later = (x + 9) years
According to question,
(x – 5) (x + 9) = 15
x² + 9x – 5x – 45 = 15
x² + 4x – 60 = 0
Therefore, the required representation in the form of quadratic equation be x² + 4x – 60 = 0.

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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

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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

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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

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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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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

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Previous Year Papers

Test Series

Test Yourself

Short Answer Type

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.

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.