CBSE Class 10 Mathematics Quadratic Equation Worksheet Set L

Quadratic Equation

Q.- Solve :

∴  x² + (x + 1)² = 61

More question- 

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)

f) x² - 5√5x + 30 = 0 (3√5, 2√5)

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 (5, 7)

c) ( k + 3 ) x² + 2 ( k + 3 )x + 4 = 0

4) For what value of p the equation (1 + p) x² + 2(1 + 2p) x + (1 + p) = 0 has coincident roots (0, -2/3)

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

a) a² x² – 3abx + 2b² = 0

b) x² – 4ax + 4a²- b²= 0 c) 6x² – 7x + 2 = 0 (2/3, ½)

6) Solve the following quadratic equations by factorization method:

a) 3x² - 2√6x + 2 = 0 (√2/3, √2/3)

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

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

9) Solve for x: 1 = 1/a+b+x = 1/a+ 1/b+ 1/x          a + b ≠ 0  (-a,-b)

10) If p, q are the roots of the equation x² – 5x + 4 =0, find the value of 1/p + 1/q - 2pq  (-27/4)

11) Solve for x: x / x +1  +x +1/x = 34/15     (3/2, -5/2)

12) Solve for x: 1/x – 3 - 1/x+5  = 1/6  (7,-9)

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

14) If x = √2 is a solution of quadratic equation x² + k x – 4 = 0, then find the value of k

15) Solve for x: 

 (-10, -1/5)

16) Solve the equation: 2(x – 3)² + 3(x – 2) (2x – 3) = 8(x + 4) (x – 4) - 1 (x =5)

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

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

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

20) The product of 3 consecutive even numbers is equal to 20 times their sum. Find the numbers (6, 8, and 10)

21) 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)

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

23) The sum of two numbers is 15 and sum of their reciprocals is 3/10. Find the numbers (5, 10)

24) 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)

25) 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)

26) The perimeter of a right angled triangle is 70units and its hypotenuse is 29 units. Find the lengths of the other sides (20, 21)

27) The length of the sides forming a right angled Δ is 5x cm and (3x – 4) cm. Area of the triangle is 60 cm2. Find the hypotenuse (17cm)

28) The length of the hypotenuse of a right angled triangle exceeds the base by 1cm and also exceeds twice the length of the altitude by 3cm. Find the length of each side of Δ (base = 12cm, hyp = 13cm, altitude = 5cm)

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

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