MATHEMATICS CLASS X

&= nbsp; &nbs= p; &= nbsp;

&n= bsp; = ; &n= bsp; &= nbsp; &nbs= p; &= nbsp; &nbs= p;

= &nb= sp; = QUADRATIC EQUATIONS

1. = If one root of the quadratic equation 2x+kx-6=3D0 is 2, find k. Also find the = other root.

2. = Solve for x

= ₌

3. = Solve for x: 3x2-14x-5=3D0

4. = Solve for x : x²–x= –a (a+1)=3D0

5. Find the value of k for which the given equation has real and equal roots.

. &= nbsp; a) 2x²-10x+k=3D0 &= nbsp;

b)_{<=
!--[if gte vml 1]>

=} =

&= nbsp; c)₌+4kx+3=3D0 <= /span>

&= nbsp; d) ₌-5x+k=3D0

e) (k= +1)x²-2(k-1)x+1=3D0

&= nbsp; f) (k-12)x²+2(k-12)x+2=3D0

6.. If -4 is a root of the quadratic equation x²+ px - 4=3D0 and the quadr= atic equation x²+px+k=3D0 has equal roots, find k.

7. = Find k for which the equation 9x²-24x+k=3D0 has equal roots.

8. = Find k for which the equation (k+4)x²+(k+1)x+1=3D0 has equal roots.

9. = If -5 is a root of the quadratic equation 2x²+px-15=3D0 and the qua= dratic equation

&= nbsp; p(x²+x)+k=3D0 has equal roots ,find k.

10. If the roots of the equation (b-c)x²+(c-a)x+(a-b)=3D0 are equal ,prove = that 2b=3Da+c

11. Solve ₌ &= nbsp;

12. ₌ &= nbsp;

13. The s= um of the squares of two consecutive natural numbers is 313. Find the numbers.

14. The s= um of two numbers is 15 if the sum of their reciprocals is₌, Find the numbers

15. A per= son on tour has Rs.360 for his expenses .If he extends his tour for 4 days he has = to cut down his daily expense by Rs.3 . Find the original duration of the tour=

16. A pie= ce of cloth costs Rs.200. If the piece was 5m longer and each meter of cloth costs Rs.2 less, the cost of the piece would be unchanged .How long is the piece = and what is the original cost of the cloth.

17. The s= peed of a boat is still water is 15 km/hr it can go 30 km upstream and return downstream to the original point in 4hr 30min.Find the speed of the stream<= /p>

18. In a = flight of 600m an aircraft was slowed down due to bad weather. Its average speed f= or the trip was reduced by 200 km/hr and the time of flight increased by 30min.Find the original duration of flight.

19. Determine whethe= r the following quadratic equations have real roots, and if so find the roots

&= nbsp; a)16x²- 24x+1=3D0

&= nbsp; b) x²+x+2=3D0

. c)₌+10x -8₌=3D0

&= nbsp; d) 3x²-2x+2=3D0

&= nbsp; e) 2x-2₌+3 =3D0

&= nbsp; f) 3a²x²+8abx+4b²=3D0

. &= nbsp; g) 3 x₌ +2₌x-5=3D0

= h) x²–2x+1=3D0

&= nbsp; i) 2x²+5₌+6=3D0

20. Two t= rains leave a railway station at th= e same time.The first train travels due West and the second train due North. The f= irst train travels 5 km/hr faster than the second train.If after 2 hours they ar= e 50 km apart find the average speed of each train.

21. A tak= es 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 wo= rk

22. Find = the whole numbers which when decreased by 20 is equal to 69 times the reciproca= l of the numbers

23. The sum of a numbers and its positive square root is 6/25.Find the numbers

24. Two numbers differ by 4 and their product is 192, find the numbers

25.. A passenger= train takes one hour less for a journey of 150 km if its speed is increased by 5 km/hr from its usual speed. Find the usual speed of the train

26. The h= ypotenuse of a right triangle is 3₌ cm .If the smaller side is tripled and the larger side is doubled, the new hypotenuse will be 15cm.Find the length of each side.

27. Find= k for real roots

&= nbsp; a) 2x²+3x+k=3D0

. &= nbsp; b) 2x²+kx+3=3D0

&= nbsp; c) 2x²-5x–k=3D0

&= nbsp; d) kx²+6x+1=3D0

&= nbsp; e) x²- kx+9 =3D0

&= nbsp; f) 4x²-3kx+1=3D0

28. Two p= ipes together fill a cistern in= minutes.If one pipe takes 3 minutes more than the other to fill the cistern= , find the time in which each pipe fills the cistern.

29. Solve= ₌

30.&= nbsp; &nbs= p; Solve ₌

31.&= nbsp; &nbs= p; Solve for x

= ₌ = given that x ₌ -3, ½

32. Solve for x

= 4 x ² - 4 a ²x + ( a⁴ – b4 ) =3D 0

33. Solve= for x

= ₌ = given that x ₌ 3, 1

34. Solve for x

= 9 x² - 9 (a= + b)x +(2 a² + 5 ab + 2 = b ²) =3D 0

37. By increasing the list price of a book by Rs 10 a person can buy 10 less books= for

Rs 1200. Find the original list price of the book. &= nbsp; &nbs= p; ( CBSE 2007)

38. The difference of two numbers is 5 and the differe= nce of their reciprocals

is 1/10. Find the numbers. &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; (CBSE 2007)

39. &= nbsp; In a class test the sum of the marks obtained by P = in Mathematics and science is 28. Had he got 3 more marks in Mathematics and 4 marks less in Science, the product of marks obtained in the two subjects wo= uld have been 180. Find the marks obtained in the two subjects separately. = ( CBSE 2008)

40. &= nbsp; The sum of the areas of two squares is 640 sq mt. If the difference in their perimeters is 64 m, find the sides of the two squares.<= span style=3D'mso-spacerun:yes'> ( CBSE 2008)

4= 1. = Find the roots of the following equation : ₌; x ₌( CBSE 2008)

ANSWERS

1. = K=3D-1, -3/2 2. 3/2, -5/2 3. 5, -1/3 = 4. -a, a+1= =

5. = a) 25/2 b). ₌ c). = ₌ &= nbsp; d). ₌ = e). 0, 3 f).<= span style=3D'mso-tab-count:1'> 12, 14

6. = 9/4 = = 7. 4/3 8. 5, -3 9. 7/4 = 11. -a , -b

12. &= nbsp; ₌ ₌ 13. 12 14. 10, 5 15. 20 days 16. 20m Rs.10/meter

17. 5 km/hr 18.<= span style=3D'mso-spacerun:yes'> 1 hour

19 a). ₌ b) not real c) -4₌

d) = not real = e). ₌ f). -₌, ₌ g) ₌ h). 1

i) &= nbsp; -2 ₌, -₌

20). 20km/hr, 15 km/hr 21. 12 days = 22. = 23

23 ). ₌

24) 12, 1= 6, (-16, -12) 25. 25km/hr 26.&nbs= p; 3cm, 6cm &nb= sp;

27 a). k₌ b) k₌k₌ c). k₌ d). k₌

e). k₌ or ₌ f). k =

28. 5, 8 minutes 29. ₌

30 5,₌ = &nb= sp; 31. x=3D -1/5, x=3D -10 32. (a ²+ b² )/2, (a ²– b²)/2=

33. x=3D -23/5 , x=3D -1 34. (2a+b)/3 , (a+2b)/3

( = 1 mark questions)

Q1. Determine = the value of k for which the quadratic equation 4x²-3kx + 1=3D0 has equal roots= . &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; (Ans: +4/3, -4/3)

Q2. Determine the value of k for which the quadratic equation kx²⁼-5x+k=3D0 has equal roots. &n= bsp; = ; &n= bsp; &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; (Ans: K=3D+5/2, -5/2)<= /p>

Q3. Fin= d the value of K for which the given equation has real and equal roots: x^{2+k(4x+k-1)+2=3D0
.       =
            &nb=
sp;                   &=
nbsp;           &nbs=
p;            &=
nbsp;        (Ans: 2/3, -1)}

Q4. Is 2x²-5x+3=3D0 a quadratic equation? I= f yes, find its roots. (Ans: Yes, 3/2,1)

Q5. Is (2x-5)-(x-8)=3D0 a quadratic equation? &= nbsp; &nbs= p; &= nbsp; (Ans: yes)

Q6. Find the values of K such that the quadratic equat= ion x²-2kx+(7k-12)=3D0 has real roots. &nb= sp; = &nb= sp; &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; (Ans: K=3D4,3)

Q7. Given= below are three equations. Two of them have infinite solutions and two have unique solutions. State the 2 pairs:

3x-2y=3D4 &= nbsp; &= nbsp; &nbs= p; <= /span>(Ans : infinite solutions-1 and = 3)
6x+2y=3D4 &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; ( unique solution-1 and 2)
9x-6y=3D12

Q8. F= or what value of K, does the quadratic equation have real and equal roots: 9x²+8k= x+16=3D0 &n= bsp; = ; &n= bsp; &= nbsp; &nbs= p; &= nbsp; ( Ans: K=3D +3,-3)

Q9. Is (2x-9)(x-1)=3D(x²-3) a quadratic equ= ation? &= nbsp; &nbs= p; = (Ans: yes)

Q10. Find the roots of 9x²-12x+4=3D0 by usi= ng the discriminant method. (Ans: x=3D2/3)

&= nbsp; = ; &n= bsp; = &n= bsp; = ; = &nb= sp;