What is the median of all values of a, for which ax^2 5x + 2 = 0 has

Question

What is the median of all values of  a , for which  ax^2 – 5x + 2 = 0  has only one solution for the variable x?

A. 0
B. 1
C. 25/16
D. 25/8
E. 25/4

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GMATinsight · Accepted Answer

CONCEPT  : For one solution of  ax^2 + bx + c = 0 , We must ensure that  b^2 - 4ac = 0

i.e. for  ax^2 – 5x + 2 = 0 ,  (-5)^2 - 4*a*2 = 0

i.e. a = 25/8

Another Possibility 
when a = 0, we'd have -5x + 2 = 0 i.e. x = 2/5

So the median  = 0+(25/8)/2 = \frac{25}{16}

Answer: Option C

RaghavKhanna · Answer

If it has only one solution
=> D = 0

=> b^2 - 4ac = 0
=> 25 - 8a = 0
=> a = 25/8

**Correction after OA was revealed**

Also, if a = 0, x = 2/5

=> Median = 25/16

=> Answer: C

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Nipungupta9081 · Answer

If it only has one solution that means D = 0 
B^2 - 4*A*C = 0
5^2 - 4*a*2 = 0
25 - 8a = 0
A = 25/8

Considering a = 0 ;then x = 2/5

Median of 0 & 25/8 = 25/16

Answer - C

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rajatchopra1994 · Answer

For only one solution, D = 0
So,

b^2 - 4ac =0
25 - 8a =0
a =25/8

Also, Consider, a = 0 ;then x = 2/5

Median of 0 & 25/8 = 25/16

IMO- D   C

Bunuel · Answer

Notice that ax^2 – 5x + 2 = 0 has one solution when a = 0 too. So, the answer is C, not D.

monikakumar · Answer

Hi  Bunuel ,

Can you please elaborate on the explanation.

Kinshook · Answer

Asked: What is the median of all values of  a , for which  ax^2 – 5x + 2 = 0  has only one solution for the variable x?

For only one solution of the equation
 ax^2 – 5x + 2 = 0 
D = 5^2 - 4*2a = 0
25 = 8a
a = 25/8

If a = 0 ; x = 2/5

Median of 0 & 25/8 = 25/16

IMO C

Bunuel · Answer

ax^2 – 5x + 2 = 0  to have only one root either the discriminant of the quadratic must be 0, which happens when a = 25/8 (check solutions above) or we should have a linear equation, which happens when a = 0 (in this case we'd have -5x + 2 = 0, which has only one solution for x, x = 2/5). So, the median value of all values of  a , for which  ax^2 – 5x + 2 = 0  has only one solution for the variable x is ((25/8 + 0)/2 = 25/16).

Answer: C.

chetan2u · Answer

For people who do not know about Discriminant, you can do this by sum of the roots and product of the roots formulas.
Product of roots =x*x=2/a
Sum of roots = x+x=-(-5/a)......x=5/2a

Substitute in product of roots =(2/a)=(5/2a)^2=25/4a^2....
a=25/8

Also a=0 will make the quadratic equation into linear equation -5x+2=0, and will have a unique value of x.

So a can be 0 or 25/8. The median will be the middle of two (0+25/8)*(1/2)=25/16

C

sambitspm · Answer

Kindly see the attachment. 
The interesting thing is to think about solutions also instead of just determinant.
C

bumpbot · Answer

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What is the median of all values of a, for which ax^2 5x + 2 = 0 has

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What is the median of all values of a, for which ax^2 5x + 2 = 0 has

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