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Quadratic Equations

Long Answer Type

11. Represent the following problem situations in the form of quadratic equations:
Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.

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12.

A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.

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Short Answer Type

13. Find the roots of the following quadratic equations by factorisation method:
x² – 3x – 10 = 0

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14. Find the roots of the following quadratic equations by factorisation method:
2x² + x – 6 = 0

2x² + x – 6 = 0
Here, a = 2, b = 1, c = –6
ac = –12 = 4 x (–3)
b = 1= 4 – 3
∴ 2x² + x – 6 = 0
⇒ 2x² + 4x – 3x – 6 = 0
⇒ 2x(x + 2) – 3(x + 2) = 0
⇒ (x + 2) (2x – 3) = 0
⇒ x + 2 = 0 or 2x - 3 = 0
⇒ x = –2 or x = 3/2
Hence, the roots of the given quadratic equation are (-2) and 3/2.

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15. Find the roots of the following quadratic equations by factorisation method:

square root of 2 straight x squared plus 7 straight x plus 5 square root of 2 equals 0

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16. Find the roots of the following quadratic equations by factorisation method:

2 straight x squared minus straight x plus 1 over 8 equals 0

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17. Find the roots of the following quadratic equations by factorisation method:

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Long Answer Type

18. John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. We would like to find out how many marbles they had to start with.

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19. A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of articles produced in a day. On a particular day, the total cost of production was Rs. 750. We would like to find out the number of toys produced on that day.

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