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A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream

Question) Jim and Tim were studying progressions and their properties. They wrote a quadratic equation, ax

^{2}- 2bx + c = 0 and assumed that a, b and c were in GP. They both had their own theories about the nature of the roots. Tim claimed that the equation had real roots and that the roots were unequal and distinct while Jim claimed that the roots were imaginary.Which of the following statements is true?

(A) Tim was correct

(B) Jim was correct.

(C) Both Tim and Jim were correct.

(D) Neither Tim nor Jim was correct.

explain componendo and dividendo....

If -4 is a root of the quadratic equation x

^{2}+px-4=k and the quadratic equation x^{2}+px+k=0 has equal roots. Find the value of k^{1}/_{4}, x not equal to 0two water taps together can fill a tank in 9(3/8 ) hours . the tap of the larger diameter takes 10 hours less than smaller one to fill the tank seprately.find the time in which each tap can seprately fill the tank.

solve;

1/a+b+x=1/a+1/b+1/x

a person goes a distance of 30 km on his bicycle. the no: of hrs taken by him is 1 hour less than his av.speed in km/hr.find the time taken by him to complete the journey.

If the roots of the equation

(a-b)x

^{2}+(b-c)x+(c-a)=0 are equal , prove that b+c=2a.1. alpha+1, alpha+6

2. alpha+1, -(alpha+6)

3. -(alpha+1), alpha+6

4. -(alpha+1), -(alpha+6)

if the roots of this equation (a2 + b2)x2 - 2(ac +bd)x + (c2 + d2)=0

are equal prove that a/b =c/d

{plz note: i was trying to put 2 as square and it wasn't working,so all the twos exept the one in b are squares }

Plz help me solving this question

solve for x:-

a/(x-a) + b/(x-b) = 2c/(x-c)

x2-2(a2+b2)x+(a2-b2)2=0

At present Asha's age is 2 more than square of her daughter Nisha's age. When Nisha grows to her mother's present age, Asha's age would be one year less than 10 times the present age of Nisha. Find the present age of both Asha and Nisha.?

Divide 19 into two parts such that the sum of their squares is 193.

solve for x :root 3x

^{2- }2 root 2x- 2 root 3=0find the value of c such that equation 4x

^{2 }- 2(c + 1)x +(c + 4) = 0 has real and equal rootsFind the positive value of k, for which the equation x

^{2 }+ kx + 64 =0 and x^{2}- 8x + k=0 will both have real roots.Find k if one root of (k-5)x² -2kx +(k-4) = 0 is less than 1 and other root is greater than 2.

the speed of a boat in still water is 15 km / hr . it can go 30 km upstream and return downstream to the orginal point in 4 hours and 30 minutes . find the speed of the stream .

Q the roots of the quadratic equation x

^{2}+5x-[a+1][a+6]=0 where a is a constant are :Two Pipes running together can fill a cistern in 3 1/13 minutes.If one Pipe takes 3 miutes more than the other to fill it, find the time in which each pipe would fill the cistern.

Seven years ago Varun's age was five times the square of Swati's age. Three years hence Swati's age will be two fifth of Varun's age. Find their present ages.

4x

^{2}+ 4bx - (a^{2}- b^{2}) = 0 please solve this equation................1. Write a quadratic polynomial whose zeroes are ( root 2 + 1) ( root 2 - 1).

2.Show that one zero of 8x

^{2}+30x+27 is the square of the other.3.If one zero of the polynomial 2x

^{2}+3x+lamda= 1/2,find the value of lamda and the other zero.A trader bought a number of articles for Rs 900. Five articles were found damaged. He sold each of the remaining articles at Rs 2 more than what he paid for it. He got a profit of Rs 80 on the whole transaction. Find the number of articles he bought.

if the difference of the roots of equation x2 +kx+12=0 is 1,then find the positive value of k

solve for x: a/ax-1 + b/bx-1 = a+b, where x is not = 1/a, 1/b. a+b is not = 0, ab is not = 0

if the roots of the equation (b-c)x

^{2}+(c-a)x +a-b=0 are equal,then prove that 2b=a+c.help me !The product of two numbers is 56. When their sum is added to the sum of their squares, we get 128. Find the numbers.

A pole has to be erected at a point on the boundary of a circular park of diameter of 13 metres in such a way that the differences of it its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. Is it possible to do so? If yes at what distances from the two gates should be pole be erected

two pipes running together can fill a tank in 11 1/9 minutes. if one pipe takes 5 minutes more than the other to fill the tank seperately , find the time taken by each pipe to fill the tank seperately .

^{2}-20(a+b)+(6a^{2}+13ab+6b^{2})=0the denominator is one more than twice the numerator , if the sum of the fraction and its recoprocal is 2 16/21 . find the fraction

if the pth term of an A.P. is 1/q and the qth term is 1/p,show that the sum of pq terms is 1/2(pq+1).

5x

^{2}-32x+48=0At 't' minutes past 2pm, the time needed by the minutes hand of a clock to show 3 pm was found to be 3 minutes less than t

^{2}/4 minutes. Find 't'.solve for x : 16x

^{2}- 8a^{2}x + (a^{4}-b^{4}) = 0A takes 6 days less than time taken by B to finish the 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

4x^2 - 16(p-q)x + 15p^2 - 34pq + 15q^2 = 0

A peacock is sitting on the top of a pillar, which is 9m high. From a point 27m away from the bottom of the pillar, a snake is coming to its hole at the base of the pillar. Seeing the snake the peacock pounces on it. If their speeds are equal, at what distance from the whole is the snake caught?

A MOTOR BOAT WHOSE SPEED IS 20KM/H IN STILL WATER, TAKES 1 HOUR MORE TO GO 48 KM UPSTREAM THAN TO RETURN DOWNSTREAM TO THE SAME SPOT FIND THE SPPEED OF THE STREAM

IF THE ROOTS OF THE EQ (a

^{2}+b^{2})x^{2}- 2(ac+bd)x + (c^{2}+d^{2})c = 0 EQUAL PROVE THAT a/b = c/d(a + b + c)the whole square

(a + b - c)the whole square

(a - b + c) the whole square

sum of the areas of two squares is 468 m

^{2}. if the difference of their perimeter is 24 m . find the sides of the squares?The length and breadth of a rectangular plot are 96m and 72m respectively. It consists of a rectangle inside it surrounded by a border of uniform width. If the area of the surrounding border is equal to the area of the inner rectangle , find the length and breadth of the inner rectangle.

6(A+B)^2X^2 + 5(a+b)cx - 6c^2 = 0

Solve BY Sridharacharya formula..

The perimeter of a right triangle is 60cm. Its hypotenuse is 25cm.Find the area of the triangle.

find the roots of equation-

ax

^{2}+a=a^{2}x+xsum of the areas of two squares is 640 m2.if the difference of their perimeters is64m,find the sides of the two squares.

Divide 41 into two positive parts such that difference of their squares is 369.If the roots of equation (c

^{2 }- ab) x^{2}- 2(a^{2}-bc) x + b^{2}-ac = 0 are equal, proove that either a=o, or a^{3}+b^{3}+c^{3}= 3abc.Pleasehelp to solve above question urgently.

for what value(s) of k does the equation x

^{2}-2kx-k = 0 will have equal roots?Q.>if x= 2/3 and x= -3 are the roots of the equation ax^{2 }+7x+b=0, find the value of a and b.The two numbers whose sum is 20 and the sum of whose cubes is 2060. We need to find the two number.

A piece of cloth costs Rs 200 .If the piece were 5m longer, and each metre of cloth costed Rs 2 less the cost of the piece would have remained unchanged. How long is the piece and what is its original rate per metre.

The ans. is 20m & Rs.10. pls give me the steps

4.2^(2x+1)-9.2^(x)+1=0

what is the formula of (a+b) whole cube

^{2}+3x +5=0 solve by factorisation and by quadratic formula method?Solve : (k+4)x

^{2}+(k+1)x +1=0 has equal roots . Find the value of k.find the nature of the roots of the equation : x

^{2 }+5x+5=0 .a train travels a distance of 480 km at a uniform speed . If the speed had been 8 km/hr less, then it would have taken 3 hrs more to cover the same distance . we need to find the speed of the train.

find the value of x :

4[x

^{2}+ 1/x^{2}] - [x + 1/x] = 60Some students planned a picnic. The budget for food was Rs. 500. But 5 of these failed to go & thus the cost of food for each student increased by Rs. 5. How many students attended the picnic?

Find the value of k for which the equation kx[x-2]+6=0 has equal roots.

Solve these equation: {(23 - 10y) / 4 }

^{2}+ y^{2 }- 4 ( 23 - 10 y ) / 4 - 3y - 1 = 0solve for x :-

(x-a)/(x-b) + (x-b)/(x-a) = a/b + b/a

A room in a hotel had been booked for Rs.1400 for new year celebrations by some boys, but 4 of them failed to reach and each of the rest of the boys had to pay Rs.40 extra. Form a quadratic equation with full explanation. We need to find the number of boys initially.

please provide me this answer

the difference of two numbers is 5 and the difference of their reciprocals is 1/10. find the no.s.....

plz show wid procedure.... answer is not comin..

If the roots of the equation (b-c)x2 +(c-a)x +(a-b) = 0 are equal than prove that

2b = c + a

in a school auditorium the number of seats in each row is 8 fewer than the number of rows...

solve by completing square:

^{x2 - (root2 + 1)x + root 2=0}A person on tour has Rs. 360 for his daily expenses. If he exceeds his tour programme by four days, he must cut down his daily expenses by Rs. 3 per day. Find the no. of days of his tour programme.

The sum of the squares of two numbers is 130. The sum of the smaller number and twice the larger number is 25. Find the numbers.

Solve for x :

9x

^{2}- 9( a + b )x + ( 2a^{2}+ 5ab + 2b^{2})Solve this by both factorisation and by using quadratic formula.

(a+b)

^{ 2}x^{2}+ 8(a^{2}- b^{2}) x +16 (a-b)^{2}= 0solve for x.

in a flight of 2800 km, an aircraft was slowed down due to bad weather. its average speed is reduced by 100km/h and time increased by 30 mins. find the original duration.

^{2}-ax+b=0 is same as the product of the roots, then find the value of (a-b)Solve : x

^{2}-(root3+1)x+root3=0 by the method of completing the square.solve

p2x2+(p2-q2)x-q2=0

a train travels 360 km at uniform speed . if the speed had been 5 km / hr more it would have taken 1 hour less for the same journey. find the speed of the train.

If the price of a book is reduced by Rs.5 ,a person can buy 5 more books for Rs.300 . Find the original list price of the article ?

Divide 31 into two parts such taht the sum of their squares is 485