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Quadratic Equations

Short Answer Type

321. The sum of the squares of two consecutive odd numbers is 394. Find the numbers.

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322. Solve the following equation for x: 9x² – (a + b)x + (2a² + 5ab + 2b²) = 0.

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323. Solve the following equation for x: 9x² – (a + b)x + (2a² + 5ab + 2b²) = 0.

Solution not provided.
Ans. $straight x equals fraction numerator 2 straight a plus straight b over denominator 3 end fraction comma space straight x equals fraction numerator straight a plus 2 straight b over denominator 3 end fraction$

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324. If- 5 is a root of the quadratic equation : 2x² + px – 15 = 0, and the quadratic equation: P(x² + x) + k = 0, was equal roots then find the value of p and k.

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325. Write the values of k for which the quadratic equation : x² – kx + 9 = 0 has equal roots.

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326. A motorboat whose speed in still water is 5 km/hr , takes 1 hour more to go 12 km upstream than to return downstream to the sauce spot. Find the speed of the stream.

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327. Sum of the areas of two squares is 260 m². If the difference of their perimeters is 24 m, then find the sides of the two squares.

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328. The age of a father is twice the square of the age of his son. Eight years hence, the age of the father will be 4 years more than three times the age of his son. Find their present ages.

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329. Write the nature of the roots of quadratic equation

4 straight x squared plus 4 square root of 3 straight x plus 3 equals 0

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Long Answer Type

330. A trader bought a number of articles for Rs. 900. Five articles were found damaged. He sold each of the remaining articles at Rs. 2 more than what he paid for it. He got a profit of Rs. 80 on the whole transaction. Find the number of articles he bought.

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