quadratic equation class 10 extra questions

(c) ≤ 0 Answer: 4y2 + 8y – 45 = 0 ⇒ y2 = 8x …..(ii) Then, the average speed of the express train = (x + 11) kmh-1 ⇒ x2 – 12x + 5x – 60 = 0 Solution. ⇒ y2 = 8 × 18 = 144 If the hypotenuse is 13 cm, find the other two sides. So, present age of Rehman = 7 yr. Let the length of base of triangle = x cm and speed of boat in up stream = (15 – x) km/H Find the speed of stream. Given, x2 – y2 = 180 …(i) ⇒ x = 20 ∴ y = 3 or 1. 50 – 5p – 15 = 0 ∴ x – y = 2 …..(i) (c) 6 (b) -2 Hence, the integer is 13. Given. So, breadth of the rectangle = 90 m and length of the rectangle = 90 + 30 = 120 m. Question 7. ⇒ 32 × 2x = (24 – x) (24 + x) ⇒ x2 – 8x – 180 = 0 New speed of the train = (x + 5) km/Hr. Neglecting the negative value of x, we have x = 13. When 2x4 – x3 – 11x2 – x + 2 = 0 According to the question, The required equation is is, Question 8. (d) 8, Question 16. ⇒ (x + 2)(2x + 1) = 0 Hence, the solutions are -2, –\(\frac{1}{2}\), \(\frac{3 \pm \sqrt{5}}{2}\). Let the total number of birds be x. ∴ y = 3 or – 5 (b) 2 ⇒ 2y2 – 6y + 5y – 15 = 0 x = 3/2 and the number of birds moving on a hill ∴ x = 5 or – 12 (c) -1, 2 Answer: According two question (d) 2 Let the breadth of the park = x metre ⇒ 2x = -8 i.e., –\(\frac {10}{3}\) ≤ x ≤ 6. (b) not real Find the number. x2 – 60x – 2700 = 0 Where ∴ 4x2 + 54x – 90 = 0 Find the roots of the equation x2 – 3x – m (m + 3) = 0, where m is a constant. ∴ Length of a rectangular mango grove = 2x metre(By given condition) (∵ In rectangle every adjacent side makes an angle 90° to each other) Answer: Question 10. (a) 1, -3 64 + x2 – 16x = 9 (6 – x) ⇒ (y + 5) (y – 3) = 0 The area of a right angle triangle is 30cm2. Then, age of other friend = (20 – x) yr Extra Questions for Class 10 Maths Chapter 4 Quadratic Equations with Solutions Answers, Question 1. Some vessels are manufactured in a day in a small industry. (a) 6 or x2 – 7x + 10 = 0 ⇒ 64x = 576 – x2 Find the width of verandah. (By factorization method) By Pythagoras theorem, we have From Eqs. ∴ 2x(x + 15) – 3(x + 15) = 0 D = b2 – 4ac . Length of verandah = (2x + 15) m. Question 6. (d) none of these. The product of the roots of quadratic equation 3x2 – 4x = 0) is: (2011OD) Solution: x2 – 3x – m(m + 3) = 0 […] (b) -3 If one root of x2 + kx + 3 = 0 is 1, then the value of k will be: (c) –\(\frac {4}{3}\) 3x + 10 = 36 + 6 – x – 12\(\sqrt{6-x}\) ∴ k = \(\frac {7}{4}\). Answer: If one root of quadratic equation ax2 + bx + c = 0 is 1, then: = k2 – 256 ≥ 0 and 64 – 4k ≥ 0 (x + 7) (d) p > 2√5 or p < – 2√5. ⇒ 200 = 225 – x2 = x(x + 44) – 33(x + 44) = 0 x + 2 x + 2 = x – 2 which is not true Product of roots = αß = (b – 2a)(b + 2a) \(\frac{2250}{x}\) = metre. (c) -4, Question 7. (d) none of these. ⇒ 2x(x + 2) + 1(x + 2) = 0 y = 6 or y = -2 Given quadratic equation are 9x + 2x + 126 √x – 18x + 1008 = 0 Squaring both sides, we get (c) 1 Solution. Hence, k = 16. State whether the equation (x + 1)(x – 2) + x = 0 has two distinct real roots or not. (a) 1, -2 Answer: (b) –\(\frac {3}{4}\) = 2(Length + Breadth)=80 m Find the positive value of k. ∴ x = 8 A dealer sells an article for ₹ 24 and gains as much per cent as the cost price of the article. (a) equal to 0 Quadratic Equations Class 10 Extra Questions Very Short Answer Type. Solution. 3x + 10 ≥ 0 and 6 – x ≥ 0 Solution. ∴ (-2)2 + 2 (-2) – p = 0 Find the two numbers. Thus, breadth of the park = 20 m (a) one zero Time taken by boat to travel 32 km in down (d) a + b + c = 0 x2 – \(\frac {1}{9}\) = 0 (d) none of these. Divide both sides by x2, ∴ x = -4 Hence, the average speed of the passenger train = 33 km/h ⇒ y2 + 3 – 4y = 0 ⇒ x2 + ax + bx + ab = 0 Question 1. and the average speed of the express train = (33 + 11) km/h = 44 km/h. ∴ x = 6 Answer: y2 – 18y – 144 = 0 ⇒ y2 – 4y + 3 = 0 Question 12. Now, x – 12 = 0 x = 12 Area of verandah = (2x + 15) (2x + 12) – 15 × 12 = 90 Hence, base of the triangle = 12 cm x2 – 4x − 21 = 0 ⇒ (x – 13)(x + 2) = 0 Question 14. The solution of quadratic equation x2 – x – 2 = 0 are: The width of verandah = 3/2 m. Question 11. (c) -4 Given quadratic equation α = b – 2a Let breadth of a rectangular mango grove = x metre ⇒ Length × Breadth = 2x (x) = 800 ⇒ y = ± 12 Solve the following quadratic equation for x: ⇒ y(y – 24) + 6(y – 24) = 0 Class 10 students definitely take this MCQ : Quadratic Equations - 1 exercise for a better result in the exam. Solve the equation If – 5 is a root of quadratic equation 2x2 + px – 15 = 0 and the quadratic equation p(x2 + x) + k = 0 has equal roots. Solution. Solve the quadratic equation (By factorization method) km = \(\frac {360}{x}\) Hours ∴ 2y2 – y – 15 = 0 (b) ≥ 0 Given, ⇒ x(x + 300) – 250(x + 300) = 0 = (3.12 – 7.5)2 (x – 4)(16 – x) = 48 …(i) Let the speed of stream be x km/h. ∴ x – y = -4 ⇒ x2 + 50x – 75000 = 0 Answer: ⇒ x2 – 13x + 2x – 26 = 0 ∴ length of its height = (x + 7) cm Question 5. x ≥ –\(\frac {10}{3}\) and x ≤ 6 We must look for solutions which satisfy x2 – x – 2 = 0 ⇒ (2x + b + a) (2x + b – a) = 0, Question 5. The square of a positive integer is greater than 11 times the integer by 26. ⇒ x2 – 18x + 10x – 180 = 0 5p = 35 ⇒ p = 7 (By fatorization method) ⇒ 2y (2y + 9) – 5(2y +9) = 0 If the roots of 5x2 – px + 1 = 0 are real and distinct, then: Given, quadratic equation The degree of the polynomial x3 – x + 7 is: Less than its base = (x – 7) cm (d) a + b + c = 0, Question 9. Find the equation whose roots are b – 2a and b + 2a. [∴ Cost Price can never be negative] If the equations x2 + kx + 64 = 0 and x2 – 8x + k = 0 have real roots. Let the required numbers be x and y, where x > y Given that – 2 is a root of given quadratic equation x2 + 2x – p = 0 4 yr ago age of one of the two friends = (x – 4) yr ⇒ (x + 12) (x – 5) = 0 Solution. Find the cost price of the article. 2x = 3 Time taken by passenger train to cover ∴ 2(-5)2 + p(-5) – 15 = 0 Let the speed of train be x km/ Hr. Solution: (x + 1)(x – 2) + x = 0 ⇒ x 2 – x – 2 + x = 0 ⇒ x 2 – 2 = 0 D = b 2 – 4ac ⇒ (-4(1)(-2) = 8 > 0 ∴ Given equation has two distinct real roots.

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