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Quadratic Equations

Short Answer Type

301. The sum of two numbers is 18. The sum of their reciprocals is

1 fourth.

Find the numbers.

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302. Solve for x: a² b² x² + b² x – a² x – 1 = 0

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Long Answer Type

303. A two digit number is such that the product of its digit is 15. If 18 is added to the number, the digits interchange their places, find the number.

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304. Using quadratic formula, solve for x: 9x² – 3(a + b)x + ab = 0

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305. Solve for x: 12abx² – (9a² – 8b²)x – 6ab = 0

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306. A train travels as a distance of 300 km at a uniform speed. If the speed of the train is increased by 5 km an hour, the journey would have taken two hours less. Find the original speed of the train.

Solution not provided.
Ans. 25 k.m./hr.

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307. Using the quadratic formula, solve the equation: a²b²x² – (4b⁴ – 3a⁴) x – 12a²b² = 0.

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308. Seven years ago Varun’s age was five times the square of Swati’s age. Three years hence Swati’s age will be two-fifth of Varun’s age. Find their present ages.

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309. A train covers a distance of 90 km at a uniform speed. Had the speed been 15 km/hour more, it would have taken 30 minutes less for the journey. Find the original speed of the train.

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Short Answer Type

310. The difference of two numbers is 5 and the difference of their reciprocals is

1 over 10.

Find the numbers.

108 Views