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Quadratic Equations

Short Answer Type

271. The perimeter of a rectangular field is 82 m and its area is 400 m². Find the breadth of the rectangle.

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272. A dealer sells an article for Rs. 24 and gains as much percent as the cost price of the article. Find the cost price of the article.

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273.

Solve for 'x': $space space fraction numerator 1 over denominator straight x plus 1 end fraction plus fraction numerator 2 over denominator straight x plus 2 end fraction equals fraction numerator 4 over denominator straight x plus 4 end fraction comma space space straight x not equal to 1 comma space minus 2 comma space minus 4$

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274. Solve the following equation by using quadratic formula:
10x² + 3bx + a² – 7ax – b² = 0.

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275. A piece of cloth costs Rs. 200. If the piece was 5 m longer and each metre of cloth costs Rs. 2 less the cost of the piece would have remained unchanged. How long is the piece and what is the original rate per metre?

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276. If boy’s age and his father’s age amount together to 24 years. Fourth part of the product of their ages exceeds the boy’s age by 9 years. Find how old they are?

Solution not provided.
Ans. 2yrs., 22 yrs.

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277. The angry Ram carried some arrows for lighting with Ravana. With 40% of the arrows, he shot down the arrows thrown by Ravana on him and with one arrow each he knocked down respectively the Rath flag, rath and bow of Ravana. With 16 other arrows he killed the rath driver of Ravana. Finally with one more than four times the square-root of arrows he killed Ravana. Find the total no. of arrows Ram had.

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278. Find the discriminant of the quadratic equation 9x² – 12x + 4 = 0, hence find the nature of its roots.

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279. For what value of k, does the quadratic equation 9x² + 8kx + 16 = 0 has equal roots?

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280. There are three consecutive positive integers such that the sum of the square of the first and the product of other two is 154. What are the integers?

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