Algebra Problems

  1. F ( x ) =such that. If -1 is root of, find the other root. ( Difficult Level )
  1. 4/3
  2. -1/3
  3. 1/3
  4. 3/4

Answer: Bacillus

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Explanation:

— — eq 1

Besides,

— — — – combining weight 2

Solving eq 1 and eq 2 we get,

and

Substitute a and B in degree Fahrenheit ( x ) = 0

or

Q. If a, B are the roots of equation, where, so happen the equation whose roots areand. ( Difficult degree )

Answer: A

Explanation:

As a and B are roots of this equation,

eq 1

eq 2

Now, the equation whose roots arewill be,

Replacing value from eq 1 and 2

Q. What will be the value of K, if equationsandhold one root in common? ( Difficult Level )

  1. 8/3
  2. 15/4
  3. -15/4
  4. – 2

Answer: Degree centigrade

Explanation:

Let P be the common root, so P will fulfill both equations.

Therefore,

eq 1

eq 2

Solving eq 2 we get,

P = 3/2 and p= 4/3

Now,

For P = 3/2

For P = 4/3

Q. The ratio of roots of the equationis r. Find the value of

( Difficult Level )

Answer: Calciferol

Explanation:

Letbe the roots, now,

=

=

=

=

=

Q. Letbe the roots of the equation, so happen the value of

( Difficult Level )

  1. 9
  2. -8
  3. 0

Answer: Bacillus

Explanation:

Let.

Now,

Therefore,

Q. The figure of roots of the equationis. ( Difficult Level )

  1. 0
  2. 1
  3. 2
  4. 3

Answer: Bacillus

Explanation:

Butwill be neglected because ( ten – 4 ) should non be less than 0.

Q. If amount of the squares of the reciprocal of the roots of equation= 0 is equal to the amount of its roots, sowill be in. ( Difficult Level )

  1. A.P.
  2. G.P.
  3. H.P.
  4. None of these

Answer: A

Explanation:

Letbe the roots, now,

Therefore,

Q. The equationandhold one root in common. If a, B, degree Celsius, so a: B: degree Celsius will be ( Difficult Level )

  1. 2: 3: 1
  2. 1: 5: 7
  3. 1: 1: 5
  4. 1: 1: 7

Answer: Bacillus

Explanation:For,

So the roots will be complex and conjugate of each other. Therefore, if one root of the given equation is common so the other will besides be same.

Now, for holding both roots common

a: B: degree Celsius = 1: 5: 7

Q.If, so k belongs to. ( Difficult Level )

Answer: Degree centigrade

Explanation:

For holding, the coefficient of ten should is positive and discriminant should be negative.

Therefore,

( k+2 ) ( k+ 6 ) & A ; lt ; 0

Q. If ratio of the roots of the equationis P: Q, so which equation is wrong? ( Difficult Level )

  1. p/q + q/p + 1 = 0
  2. P + Q + 1 = 0

Answer: Bacillus

Explanation:

For

Therefore, its roots will be fanciful.

Let the fanciful roots be

For A,

. So A. is right.

For B,

.So B. is wrong.

Q. If the roots of the equationare existent and less than 3, so

( Difficult Level )

  1. K & A ; lt ; 3
  2. K & A ; gt ; 4

Answer: A

Explanation:

For both roots less than 3,

Uniting consequences from I, two and three we get, k & A ; lt ; 3

Q. If the roots of the equationprevarications on either side the beginning, so happen the value K lies in ( Difficult Level )

Answer: Calciferol

Explanation:

For holding roots on both sides of the beginning,

Q. Find the value of Q for which precisely one root of the equationprevarications between 1 and 2. ( Difficult degree )

  1. ( -1,0 )
  2. ( 1,2 )
  3. ( -1,2 )
  4. None of these

Answer: A

Explanation:

For holding precisely one root between 1 and 2,

Let

Q. Ifare the roots of a quadratic equation such that, the equation will be ( Difficult Level )

  1. Both A and B
  2. None of these

Answer: Degree centigrade

Explanation:

Square cant be negative, so ignored.

Therefore, the needed equation will be

Q. Ifandare the roots of the equation, so ( Difficult Level )

Answer: Calciferol

Explanation:

Sum of roots =

Squaring both sides,

{ merchandise of roots = r/p }

Q. If equationhas one root common with the equationso( Difficult Level )

  1. 2
  2. -1
  3. 1
  4. None of these

Answer: Bacillus

Explanation:

Acc. to ques,

Q. Two back-to-back even natural Numberss are such that amount of their squares is 340. Find the geometric mean of the Numberss. ( Difficult Level )

  1. None of these

Answer: A

Explanation:

Two back-to-back even natural Numberss can be assumed as ten and ( x+2 )

Now,

Now the geometric mean will be

Q. In a school park, out of entire kids, one 4th are playing on swings, 1/9Thursdayare playing coupled with 1/4Thursdaymore, 7 times the square root of the sum are playing cricket, while 56 are listening to a story-teller. How many kids are at that place in the park in park?

( Difficult Level )

  1. 144
  2. 368
  3. 576
  4. 287

Answer: Degree centigrade

Explanation:

Let x be the entire figure of kids.

Acc. to ques,

Squaring both sides,

( neglected because 56 kids were with story-teller )

Therefore, x = 576

Q. If -3 and P are the roots of the quadratic equation, so

( Difficult Level )

  1. None of these

Answer: Bacillus

Explanation:

Harmonizing to ques,

Sum of roots =

eq 1

Besides,

Merchandise of roots =

Put value in eq 1

Now, P ( 2 ) = 1

Q.For two existent Numberss a and B, the equationWhich of the statement is true? ( Difficult Level )

  1. None of these

Answer: A

Explanation:

Rewriting the equation,

For a be existent,

Again rewriting the given equation,

For B be existent,

Q. The curveintersects x-axis at ( a,0 ) and ( b,0 ) . If a and B are whole numbers, what is the minimal value of K? ( Difficult Level )

  1. -164
  2. -165
  3. 4
  4. 0

Answer: Bacillus

Explanation:

Clearly, a and B are the roots of the given equation.

Sum of roots = a + B = -k

Therefore, to do K lower limit, the amount of roots should be maximal.

Besides,

Merchandise of roots = a ten B = 164

As a and B are both whole numbers, therefore they will be built-in factors of 164.

Possible built-in factors:

1 x 164

2 x 82

4 x 41

Now the factors with soap amount are 164 and 1

Therefore the minimal value of K = – ( 164 +1 ) = -165

Q. For a quadratic equationthe roots are two distinguishable whole numbers. How many values are possible for ‘b’ ? ( Difficult Level )

  1. 4
  2. 6
  3. 2
  4. 1

Answer: Bacillus

Explanation:

The possible values of B will be the figure of ways 92 can be split into built-in multiples.

The possible built-in factors of 92 are ( 1, 92 ) , ( 2, 46 ) , ( 4,23 ) . Besides the negative brace will besides hold same merchandise.

Therefore, a sum of 6 combinations exists which will be holding their merchandise equal to 92.

Sum of roots = -b

There will be 6 distinguishable amount possible with 6 distinguishable braces.

Hence, B can hold 6 possible values.

Q. For what values of K is y=0, iften is a existent figure.

( Difficult Level )

  1. None of these

Answer: Degree centigrade

Explanation:

Rewriting the equation,

If x is existent figure, so the discriminant of the equation will be greater than equal to 0.

Q. The roots of the equationareFind the quadratic equation whose roots are( Difficult degree )

Answer: Calciferol

Explanation:

Acc. to ques,

The needed equation will be

Q. The difference between the roots of the equationis atleast 12. What is the scope of values for K? ( Difficult Level )

  1. Both A and C

Answer: Calciferol

Explanation:

Letbe the roots of the equation.

Now,and

As the difference of roots is atleast 12,

Q. Suresh is 4 old ages younger to Ramesh. 7 old ages ago, Ramesh’s age was 2 more than square of Suresh’s age. How old Ramesh will be after 4 old ages from now. ( Medium Level )

  1. 17
  2. 13
  3. 10
  4. 15

Answer: A

Explanation:

Let Ramesh’s age be x. so Suresh’s age will be ( x-4 )

Seven old ages ago,

Therefore Ramesh’s age after 4 old ages will be ten +4 = 17 or 14

Q. The graph of the quadratic equationis wholly above X-axis if. ( Medium Level )

  1. None of these

Answer: Degree centigrade

Explanation:

If the graph is wholly above X-axis so the equation must non hold any existent root.

Q. For what value p the harmonic mean of the roots of the equationwill be -3. ( Medium Level )

  1. 7
  2. -3
  3. 1
  4. None of these

Answer: Calciferol

Explanation:

Let the roots of the equation be.

Acc. to ques.= – 3

= -3

= – 3

P = -2

Therefore reply will be D.

Q. One of the roots of the equationis square of the other. If K & A ; gt ; 0, find the value of. ( Medium Level )

  1. 4/9
  2. 1/9
  3. 36
  4. 1

Answer: Degree centigrade

Explanation:

Letbe the roots.

Now,

Besides, Sum of roots =

eq 1

Merchandise of roots =

Put value ofin eq 1

Q. If the difference of roots of the equationis equal to the merchandise of the roots, so ratio of the roots will be. ( Medium Level )

Answer: Calciferol

Explanation:

Letbe the roots, now,

{

Put value ofin

Q. In a right angled triangle, the hypotenuse is 3 more than twice of the smallest side. If the 3rd side is, so the hypotenuse is. ( Medium Level )

  1. 13
  2. 17
  3. 23
  4. None of these

Answer: A

Explanation:

Let smallest side be x,

Acc. to Pythagoras theorem,

The hypotenuse will be

Q. If, the value of( Medium Level )

  1. 1
  2. 2
  3. -1
  4. 0

Answer: A

Explanation:

Dividing the equation by

Q. One of the roots of the quadratic equationwill be

( Medium Level )

  1. p/q
  2. –r/p
  3. q/r
  4. None of these

Answer: Calciferol

Explanation:

Q. The roots of the equationare ( Medium Level )

  1. 2,4
  2. 1,0
  3. -1, 4
  4. None of these

Answer: A

Explanation:

Q. If ten =2 is one of the roots of the equation, where K is a changeless. Find the 2nd root of the equation. ( Medium Level )

  1. 0
  2. 1
  3. -2
  4. -1

Answer: Degree centigrade

Explanation:

If ten =2 is one root, so it should fulfill the equation.

Now, the equation becomes

Therefore the 2nd root is ten =-2.

Q. The amount of a figure ten and its mutual is equal to 13/6. Find the value of x given x & A ; gt ; 1.

( Medium Level )

  1. None of these

Answer: Bacillus

Explanation:

Harmonizing to the inquiry,

Q. Find the value of Ps such that the equationhas merely one solution given that P & A ; gt ; 0.

( Medium Level )

  1. 1
  2. 2
  3. -1
  4. -2

Answer: Degree centigrade

Explanation:

For holding merely one solution,

Q. If the difference between the roots of the equationbe 1, so:

( Medium Level )


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