# Algebra – 16

## 14 thoughts on “Algebra – 16”

1. Siddharth Sekhar |

Hi catcracker! I have a question.
For question 1, after you have proved that ‘c’ can only take only value – 1,
in the alternate method, you have solved using options.
In general, if CBD is one of the options, can we still solve using options?
If I find 1 option that satisfies the conditions, wouldn’t I still have to ensure that no other values can satisfy the equation?

Thanks for the wonderfully detailed posts!

• Normally, no. But in this case if 1 satisfies and 2 doesn’t, then 3, 4, etc will also not satisfy, wouldn’t you agree?

regards
J

• Siddharth Sekhar |

Ah yes, because the value of ‘a’ would keep decreasing.
Thank you!

2. Siddharth Sekhar |

Sir,

Can you help me with this question discussed in IMS CAT workshop?

Find the number of positive roots of f(x) = a*x^2 + b*x + c ( a not equal to 0) .

Conditions given : 1. f(x) has real roots
2. c > 0
3. the minimum value that f(x) can take is 9a + 3b + c.
Options : 1) 0 2) 1 3) 2 4) 1 or 2

My solution : From condition 3 , we see that minimum value is at x = 3.
So the roots must be symmetrical about 3.
For eg: 2 and 4 ( where both roots are positive)
-1 and 7 ( where only 1 is positive)

Therefore, it is option 4.

The official answer was option 2 ( I only thought of this now, while at home).
Is my approach/answer right? Would you suggest substituting different values of roots for questions such as these?

• The official answer was not option 2 but option 3 (value 2). The thing is it is asking for POSITIVE roots. In the case you gave of -1 and 7 as roots, c would be negative (think about it!). Both roots will have to be positive.

regards
J

• Siddharth Sekhar |

Ok, I got it..to have a minimum value, it must be an upward drawn parabola ( a> 0) , but product of roots is negative.
Thank you sir! ðŸ™‚

3. Gaurav |

Sir,
Could you post topics about questions to do with different types of minimum and maximum questions? I have been trying to search, but, couldn’t find those many to solve. It would be really helpful if you could or suggest a website that has those types of questions.
Thank You

4. I don’t know of any such source. I have posted a few very basic ones, but the very fancy ones rarely come in the exam so I haven’t bothered too much. (And this year, I am not getting any spare time to research and post….have already posted on all the main topics where I had something useful to say)

regards
J

5. Hello,

I tried solving question no. 2 without putting in options. Just like the way you answered question no. 1.

Could you please correct where I went wrong as I ain’t getting 13 as an answer.

Given – Section C has 8 questions and there are 100 questions

Solution:

a+b = 92

Case –
Section A contains at least 60% of total marks and Section B contains at least 20% of total marks
means, a>=3/5(a+2b+3c) and b>=1/5(a+2b+3c)
means, 5a>=3(92 + b + 24) and 5b >= 92 + b + 24
means, 5(92 – b) >= 348 + 3b and 5b >= 116 + b
means, 8b=116
means, b=29

How is this possible if both the conditions about the least % of marks from Section A and B have to be true?

Also, how would I know what is the answer if it was asked as a TITA question, ex – write the sum of both possible options for number of questions in section B.

Looking forward towards your reply J and T.

PS – your blog is amazing..!!

Thank you. ðŸ™‚

• i meant
means, 5(92 â€“ b) >= 348 + 3b and 5b >= 116 + b
means, 8b=116
means, b=29

how is this possible?

• I think the error is here “b>=1/5(a+2b+3c)” because the marks for b questions are 2b. so it should have been “2b>=1/5(a+2b+3c)”. See whether that gives you a correct answer?

regards
J

• YES…I got b>=12.9 in one case and b<=14 in another.

Thanks J for the quick revert. ðŸ™‚

6. Hi Sir, would you consider this question as Type B or Type C?

• Since there were 2 questions and hence twice the marks, I think it would give value for money for the time spent. Hence, B.

regards
J