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Mathematics : Quadratic Equations

Short Answer Type

281. An aeroplane takes 1 hour less for a journey of 1200 km if its speed is increased by 100 km/hr from its usual speed. Find its usual speed.

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282. A passenger train takes 3 hours less for a journey of 360 km if its speed is increased by 10 km/hour from its usual speed. What is its usual speed?

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283. A passenger train takes 3 hours less for a journey of 360 km if its speed is increased by 10 km/hour from its usual speed. What is its usual speed?

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284. If – 5 is a root of the quadratic equation 2x² + px – 15 = 0 and the quadratic equation p(x² + x) + k = 0 has equal roots, find the value of k.

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285. Determine value(s) of p for which the quadratic equation 4x² – 3px + 9 = 0 has real roots.

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Long Answer Type

286. The distance between Mumbai and Pune is 192 km. Travelling by Deccan Queen, it takes 48 minutes less than another train. Calculate the speed of the Deccan Queen if the speed of the two trains differ by 20 km/hr.

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287. A farmer wishes to grow a 100 m² rectangular vegetable garden. Since he has with him only 30 m barbed wire, he fences three sides of the rectangular garden letting compound wall of his house act as the fourth side-fence. Find dimensions of his garden.

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Short Answer Type

288. Determine value(s) of p for which the quadratic equation 2x² + 3x + p = 0 has real roots.

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Long Answer Type

289. The length of the hypotenuse of a right angled triangle exceeds the base by 1 cm and also exceeds twice the length of the altitude by 3 cm. Find the length of each side of triangle.

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290. If twice the area of smaller square is subtracted from the area of a larger square, the result is 14 cm². However, if twice the area of the larger square is added to three times the area of the smaller square, the result is 203 cm². Determine the sides of squares.

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