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27 Apr 2010, 14:47
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I have gathered some quadratic questions that are within the scope of the GMAT. Detailed Explanations are appreciated.
1. If
then the value of x is
a) 13/4
b) -5/2
c) -7/2
d) 9/2
e) 17/2
2. In writing a quadratic equation of the form
, a student writes the coefficient of incorrectly and finds the roots as 7 and 8. Another student makes a mistake in writing the constant term and gets the roots as 8 and -3. Find the correct quadratic equation:
a)
b)
c)
d)
e)
3. If the sum and product of the roots of the equation
are equal then:
a)
b)
c)
d)
e)
4. If one root of
is the square of the other, then is
a) 5
b) 6
c) -6
d) 7
e) -7
5. In the interior of a forest, a certain number of apes equal to the square of one-eighth of the total number are playing and having great fun. The remaining twelve apes are on a hill and the echo of their shrieks by the adjoining hills frightens them. They came and join the apes in the forest and play with enthusiasm. What is the total number of apes?
a) 48
b) 16
c) 64
d) 80
e) -16 or 48
6. What can you say about the roots of
A. One root is double the other.
B. One root is the square of the other.
C. One root is the reciprocal of the other.
D. The roots are equal in magnitudes but differ in signs.
E. None of These
7. The quadratic equation, whose roots are reciprocal of the roots of
, is:
a)
b)
c)
d)
e)
8. If the roots of the equation
are in the ratio 
, then the value of 
is
a)
b)
c)
d)
e)
1. If
a) 13/4
b) -5/2
c) -7/2
d) 9/2
e) 17/2
2. In writing a quadratic equation of the form
a)
b)
c)
d)
e)
3. If the sum and product of the roots of the equation
a)
b)
c)
d)
e)
4. If one root of
a) 5
b) 6
c) -6
d) 7
e) -7
5. In the interior of a forest, a certain number of apes equal to the square of one-eighth of the total number are playing and having great fun. The remaining twelve apes are on a hill and the echo of their shrieks by the adjoining hills frightens them. They came and join the apes in the forest and play with enthusiasm. What is the total number of apes?
a) 48
b) 16
c) 64
d) 80
e) -16 or 48
6. What can you say about the roots of
A. One root is double the other.
B. One root is the square of the other.
C. One root is the reciprocal of the other.
D. The roots are equal in magnitudes but differ in signs.
E. None of These
7. The quadratic equation, whose roots are reciprocal of the roots of
a)
b)
c)
d)
e)
8. If the roots of the equation
a)
b)
c)
d)
e)
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27 Apr 2010, 19:09
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Here are the ans from my end
1. C
2. B
3. B
4. C
5. B
6. C
7. C
8. B
Can you please confirm the ans
Explanation
1. considering x as non-zero the equation will reduce to
1/x+3 +1/x+4 = 1/x+2 +1/x+5
or 1/x+3 - 1/x+2 =1/x+5 -1/x+4
solving x=-7/2
2. sum of the roots =-b =8-3 or 5
product of the root =7*8=56
3.sum of the root=product of the root
i.e b=c
4. sum of the root k/8= -(a+a^2)...where a is the root
product of the root =1/a^3=1/8 or a=1/2
5. used the options to find the ans
6. if a and b are the roots then ab=p/p=1
7.if a,b are the roots then a+b=-3/2 and ab=-1
we need to find the equation
x^2 +(a+b/ab)x+1/ab=0
8.if roots are r1,r2
r1+r2=-r/p and r1r2=r/p
the first one took more than 2 minutes for me.better approach will be really appreciated.
1. C
2. B
3. B
4. C
5. B
6. C
7. C
8. B
Can you please confirm the ans
Explanation
1. considering x as non-zero the equation will reduce to
1/x+3 +1/x+4 = 1/x+2 +1/x+5
or 1/x+3 - 1/x+2 =1/x+5 -1/x+4
solving x=-7/2
2. sum of the roots =-b =8-3 or 5
product of the root =7*8=56
3.sum of the root=product of the root
i.e b=c
4. sum of the root k/8= -(a+a^2)...where a is the root
product of the root =1/a^3=1/8 or a=1/2
5. used the options to find the ans
6. if a and b are the roots then ab=p/p=1
7.if a,b are the roots then a+b=-3/2 and ab=-1
we need to find the equation
x^2 +(a+b/ab)x+1/ab=0
8.if roots are r1,r2
r1+r2=-r/p and r1r2=r/p
the first one took more than 2 minutes for me.better approach will be really appreciated.
Very nice,
Answers:
1. C- The way I solved it was reducing down to (7/X) + 2 = (7/X) + 2. Use the answers to plug in.
2. B- reasoning correct
3. B
4. C
5. E
6. C
7. A
8. B
Answers:
1. C- The way I solved it was reducing down to (7/X) + 2 = (7/X) + 2. Use the answers to plug in.
2. B- reasoning correct
3. B
4. C
5. E
6. C
7. A
8. B
