Two different quadratic equations have a com...
Two different quadratic equations have a common root. Let the three unique roots of the two equations be A, B and C - all of them are positive integers. If (A + B + C) = 41 and the product of the roots of one of the equations is 35, which of the following options is definitely correct?
• a)
The common root is 29.
• b)
The smallest among the roots is 1.
• c)
One of the roots is 5.
• d)
Product of the roots of the other equation is 5.
• e)
All of the above are possible, but none are definitely correct.
Two different quadratic equations have a common root. Let the three u...
It has been given that A+B+C = 41.
Let the common root be B.
All the roots are positive integers.
The product of the roots of one of the equations is 35.
35 can be obtained only in 2 ways - either as 5*7 or 35*1.
A+B+C = 41.
If A and B are 5 and 7 in any order, then C = 41 - 5 - 7 = 29.
If A and B are 35 and 1 in any order, then C = 41 - 35 -1 =5.
As we can see, in either case, 5 is one of the 3 roots.
Therefore, option C is the right answer.
Two different quadratic equations have a common root. Let the three u...
Given information:
- Two different quadratic equations have a common root.
- The three unique roots of the two equations are A, B, and C, all of which are positive integers.
- (A + B + C) = 41.
- The product of the roots of one of the equations is 35.

To determine the correct option, we need to analyze the given information.

- Let's assume the two quadratic equations are:
Equation 1: ax^2 + bx + c = 0
Equation 2: px^2 + qx + r = 0

- Since the equations have a common root, this means that the common root satisfies both equations. Let's call the common root 'k'.

- Therefore, substituting 'k' into both equations, we get:
ak^2 + bk + c = 0
pk^2 + qk + r = 0

- Since k is a root of both equations, these equations can be factored as:
a(x - k)(x - m) = 0
p(x - k)(x - n) = 0

- From the first equation, we can infer that the product of the other two roots (m and n) is c/a.
- From the second equation, we can infer that the product of the other two roots (m and n) is r/p.

- Since the product of the roots of one of the equations is 35, we can conclude that either c/a = 35 or r/p = 35.

- Let's consider the options given:
a) The common root is 29.
b) The smallest among the roots is 1.
c) One of the roots is 5.
d) The product of the roots of the other equation is 5.
e) All of the above are possible, but none are definitely correct.

- Let's analyze each option based on the given information:

a) The common root is 29:
- We cannot determine if this is true or false based on the given information.

b) The smallest among the roots is 1:
- We cannot determine if this is true or false based on the given information.

c) One of the roots is 5:
- This option is definitely correct because it is given that all the roots are positive integers. So, one of the roots can be 5.

d) The product of the roots of the other equation is 5:
- We cannot determine if this is true or false based on the given information.

e) All of the above are possible, but none are definitely correct:
- This option is not correct because option c is definitely correct, as explained above.

Therefore, the correct option is c) One of the roots is 5.
 1 Crore+ students have signed up on EduRev. Have you?
1 Crore+ students have signed up on EduRev. Have you?

Learn this topic in detail

 Test: XAT Quant 2018 27 Ques | 40 Mins
 More from Related Course Quantitative Aptitude (Quant)
 View courses related to this question

850+
Video Lectures
2500+
Revision Notes
600+
Online Tests
34+
Courses
Two different quadratic equations have a common root. Let the three unique roots of the two equations be A, B and C - all of them are positive integers. If (A + B + C) = 41 and the product of the roots of one of the equations is 35, which of the following options is definitely correct?a)The common root is 29.b)The smallest among the roots is 1.c)One of the roots is 5.d)Product of the roots of the other equation is 5.e)All of the above are possible, but none are definitely correct.Correct answer is option 'C'. Can you explain this answer?
Question Description