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Sk Coaching Dumka, , CLASS-X, MATHEMATICS WORKSHEET, CHAPTER-4: QUADRATIC EQUATIONS, VERY SHORT ANSWER TYPE QUESTIONS, Q1. Show that x = -3 is the solution of the equation x2 +6x +9 = 0., Q2. For what value of k are the roots of quadratic equation 3x2 +2kx +27 = 0 real and equal?, Q3. Write the nature of roots of quadratic equation 4x2 +4√3x +3 = 0., Q4. If a and b are the roots of the equation x2 +ax –b = 0, then find a and b., Q5. If x = 3 is one root of the quadratic equation x2 – 2kx -6 = 0, then find the value of k. (CBSE 2018), Q6. Which of the following are quadratic equations, a) x3 –x = x2 +2, b) √x +4 = x +1, c) (x +1)(x2 -2) = (x +3)3, SHORT ANSWER TYPE QUESTIONS, Q7. Solve for x:, Sk Coaching Dumka, a) x2 -2(a2 +b2 )x + (a2 –b2 )2 = 0, b) 2x2 +ax –a2 = 0, c) p2 x2 +(p2 – q2 )x –q2 = 0, d) √2x2 +7x +5√2 = 0, e) (a +b)2 x2 +8(a2 – b2 )x +16(a – b)2 = 0, f) 1/(a +b +x) = 1/a + 1/b + 1/x, a≠ 0, b≠ 0, x≠ 0., Q8. If ad ≠ bc, then prove that the equation (a 2 +b2 )x2 +2(ac +bd)x +(c2 +d2 ) = 0 has no real roots., Q9. If sinθ and cosθ are roots of the equation ax2 +bx +c = 0, prove that a2 –b2 +2ac = 0., Q10. If one root of the equation 3x2 –kx -2 = 0 is 2, find the value of k. Also find the other root., Q11. 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., Q12. Find the value of k for which the roots of the quadratic equation (k -4)x2 +2(k -4)x +2 = 0 are equal., Q13. Find the value of k for which the equation x2 +kx +64 = 0 has real roots., Q14. If the roots of the equation (b –c)x2 + (c –a)x + (a –b) = 0 are equal then prove that 2b = a + c., Q15. If the roots of the equation (c2 –ab)x2 – 2(a2 –bc)x + b2 -ac = 0 are equal, then prove that either a = 0 or, a3 +b3 +c3 = 3abc., Q16. If the roots of the equation (1 +m2 )x2 +2mcx +(c2 –a2 ) = 0 are equal, then prove that c2 = a2 (1 +m2 )., LONG ANSWER TYPE QUESTIONS, Q17. A train travels at a certain average speed for a distance of 63km and then travels at a distance of 72km, at an average speed of 6km/hr more than its original speed. If it takes 3 hours to complete total, journey, what is the original average speed? (CBSE 2018), Q18. An aeroplane left 30 minutes later than its scheduled time and in order to reach its destination 1500km, away in time, it has to increase its speed by 250 km/hr from its usual speed, determine its usual speed., (CBSE 2018), Q19. Two water taps together can fill a tank in 1⅞ hours. The tap with longer diameter takes 2 hours less, than the tap with smaller one to fill the tank separately. Find the time in which each tap can fill the, tank separately. (CBSE 2019), Q20. A takes 6 days less than the time taken by B to finish a piece of work. If both A and B together can, finish the work in 4 days, find the time taken by B to finish the work., Q21. (a) (x +1)/(x -1) + (x -2)/(x +2) = 3, x≠1, -2, (b) (3x -4)/7 + 7/(3x -4) = 5/2, x≠ 4/3, , 1