CBSE Class 10 Mathematics Quadratic Equation Worksheet Set K

Quadratic Equation

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1) Find the discriminate of the quadratic equation: 3 √3 x² + 10x + √3 = 0 (64)

2) Solve for x: a) 9x² – 9 (a + b) x + 2a² + 5ab + 2b² = 0 (2a+b/3, a + 2b/3)

b) 4x² – 4a2x + (a⁴– b⁴) = 0 (a² +b²)/2, (a²- b²)/2

c) 10ax² – 6x +15ax – 9 = 0 (-3/2, 3/5a)

d) x2 – 2(a² + b² )x + (a² – b²)² = 0 (a+b)², (a-b)²

e) √7x² – 6x – 13 √7 (13√7/7, - √7)

3) find the value of k so that the quadratic equation has equal roots:

a) 2kx² – 40x + 25 = 0 (k = 8)       b) 2x² – (k – 2) x + 1 = 0 (2+2√2)

c) K x (x – 7) + 49 = 0 (0, 4)          d) (k -5)x² + 2(k-5)x + 2 = 0 (5,7)

4) Find the roots of the following quadratic equation by the method of completing the Square.

a) a²x² – 3abx + 2b² = 0    b) x² – 4ax + 4a²- b²= 0

5) Solve the following quadratic equations by factorization method:

a) 3x² - 2√6x + 2 = 0 (√2/3, √2/3) b) 9x² – 6ax + (a² – b²) = 0 (a² + b² , a² – b²)

3 2

6) write the nature of roots of quadratic equation: 4x² + 4√3x + 3 = 0

7) Check whether the equation x³ – 4x² + 1 = (x – 2)² is quadratic or not

8) Solve for x: 1 = 1 + 1 + 1, a + b ≠ 0

a + b + x a b x (-a, -b)

9) If p, q are the roots of the equation x² – 5x + 4 =0, find the value of 1 + 1 - 2pq

P q (-27/4)

10) Solve for x: x + x +1 = 34 (3/2, -5/2)

x + 1 x 15

11) Solve for x: 1 - 1 = 1 (7,-9)

x – 3 x + 5 6

12) If one root of a quadratic equation 3x²+ PX + 4 = 0 is 2/3, find the value of p (p = -8)

13) Solve for x: 2 2x -1 – 3 x +3 = 5

X+3 2x-1 (-10, -1/5)

14) The sum of the squares of two consecutive odd numbers is 394. Find the numbers. (13, 15)

15) The sum of the areas of two squares is 640 m2. If the difference in their perimeter is 64m .Find the sides of the two squares (8m, 24m)

16) The difference of two numbers is 4. If the difference of their reciprocals is 4/21, find the numbers (3, 7)

17) A plane left 30 minutes late than its scheduled time and in order to reach the destination 1500km away in time it had to Increase the speed by 250 km/h from the usual speed. Find its usual speed (750 km / hr)

18) The hypotenuse of a grassy land in the shape of a right triangle is 1m more than twice the shortest side. If the third side is 7m More than the shortest side find the sides of grassy land ( 8, 15)

19) Find two consecutive numbers, whose squares have the sum 85. (6, 7)

20) The sum of the reciprocals of rehmans age 3years ago and 5years from now is 1/3, find his present age

21) A natural number, when increased by 12, becomes equal to 160 times its reciprocal. Find the number (8)

22) 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 it in 4 days; find the time taken by B to finish the work (12 days)

23) The speed of a boat in still water is 15 km/hr. It can go 30km upstream and return downstream to the original point in 4hrs 30min. Find out the speed of the stream (5km/hr)

24) A two digit number is such that the product of its digits is 18. When 63 is subtracted from the number, the digits interchange their places. Find the number (92)

25) Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20years.Four years ago, the product of their ages was 48. (D = - 48, No)

26) If the roots of the equation (b – c) x² + (c – a) x + (a – b) = 0 are equal, then prove that 2b = a + c

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