Problems on Algebric Expressions

Problems on Algebric Expressions

Learn and practice Problems on Algebric Expressions with easy explaination and shortcut tricks. All questions and answers on Algebric Expressions covered for various Competitive Exams.

Solve Problems:

1) If x2 +1/ x2 = 34,x+1/x is equal to

  1. 3
  2. 4
  3. 5
  4. None of these
View Answer

Answer: D

Explanation:

Adding 2 to the L.H.S and R.H.S of the equation:

x2+2+=34+2[∵(a+b)2=a2+b2+2ab]

(x+)2= 36

(x+)= +6,-6

2) The value of x in the equation: 16x +1/x = 8 is

View Answer

Answer: A

Explanation:

16x+=8

=8

16x2+1=8x

=>16x2+1-8x=0

=>(4x-1)2=0

=>x =1/4 , 1/4

3) The equation whose roots are 4 and 5, is

  1. x2+9x-20=0
  2. 0= x2+9x+20
  3. x2-9x+20=0
  4. x2-9x-20=0
View Answer

Answer: C

Explanation:

The required equation is:
x2-(sum of roots)x+product of roots=0
=>x2-(4+5)x+4 ×5=0
=>x2-9x+20=0

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4) The perimeter of a rectangle is 48 meters, and its area is 135 m2. The sides of the rectangle are

  1. 15 m, 9m.
  2. 19m, 5m.
  3. 45m, 3m.
  4. 27m, 5m.
View Answer

Answer: A

Explanation:

Let the sides of the rectangle be x and y meters respectively. Then
2x + 2y = 48
2 (x+y) = 48
x+y = 24
y = 24 -x

We have, xy = 135
So, x (24 – x) = 135
24x – x2 = 135
x2 -24x + 135 = 0
x2 – 9x – 15x + 135 = 0
(x-9) (x -15) = 0
x = 9 m or 15 m
So, when x = 9m, y = 24 – 9 = 15m
And when x = 15, y = 24 -15 = 9 m
So, the sides of rectangle are 15m and 9m.

5) The roots of the equation (x + 3) (x – 3) = 160 are

  1. + 13
  2. 13, 13
  3. + 12
  4. 12, 12
View Answer

Answer: A

Explanation:

(x + 3) (x – 3) = 160
x2 – 9 = 160
x2 = 169
x = +13, – 13

6) The solution of 

  1. 1/8
  2. -1/8
  3. 8/3
  4. -8/3
View Answer

Answer: B

Explanation:

Given equation is
(2x+3) (3x+1) = (3x-1) (2x-1)
= 6x2 + 11x + 3
= 6x2 – 5x + 1
= 16x +2
16x = -2
x = -1/8

7) If the equation 4x2+x(p+1)+1=0 has exactly two equal roots, one of the value of p is

  1. 5
  2. -3
  3. 0
  4. 3
View Answer

Answer: D

Explanation:

Roots are equal if discriminant
b2 – 4ac = 0
In given equation:
(P+1)2 – 4.41 = 0
(p+1)2 = 16 = (4)2
p+1 = +4, -4
p= 3 or – 5

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8) A journey of 300 km takes two hours more when the speed of a care is reduced by 5km/hr. What is the original speed of the car?

  1. 30
  2. 40
  3. 70
  4. 80
View Answer

Answer: A

Explanation:

Let the speed of the car is x km/hr. Then
Speed = distance/ time:

=2

=>

x2 – 5x – 750 = 0
x2 – 30x + 25x – 750 = 0
(x – 30) (x + 25) = 0
x =30 or x = -25
The negative value of x is inadmissible; therefore the speed of the car is 30 km/hr.

9) The solution for

  1. -5
  2. -1
  3. -3
  4. 3
View Answer

Answer: A

Explanation:

The given equation:

x2 – 3x – 4x -12 = – 6x +18
x2 – x – 30 = 0
x2 + 5x – 6x – 30 = 0
(x+5) (X-6) = 0
x = – 5 or 6

10) If x2+ax+b=0 and x2+bx+a=0 is double the other; a, b, c are related as

  1. 2a2 = 9bc
  2. 9a2 = 2bc
  3. 2b2 = 9ac
  4. 9b2 = 2ac
View Answer

Answer: C

Explanation:

If α and β be the roots of the equation:
Then α + β = , and αβ =

Also, α = 2β. Then
3β==>β =

And,
2β2=

∴

=>=

=>2b2=9ac

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