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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.

Let Rohan's present age = x years.
Then, Rohan’s mother age = (x + 26) years
Rohan’s age after 3 years = (x + 3) years and Rohan’s mother age after 3 yrs.
= (x + 29) years.
According to the given condition, (x + 3) (x + 29) = 360
⇒ x² + 32x – 360 =0
⇒ x² + 32x – 273 = 0
⇒ x² + 39x – 7x – 273 = 0
⇒ x(x + 39) – 7(x + 39) = 0
⇒ (x + 39) (x – 7) = 0
⇒ x = –39 or x – 7 = 0 But age cannot be –ve.
∴ x = 17
Hence, Rohan's present age = 7 years.

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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

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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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