If f(5 + x) = f(5 - x) for every real x | Quantitative Aptitude - CAT Progression

You may also find remaining question solution of CAT 2020, slot 1 by searching the question in the search bar.

The question below is from previous year CAT question from CAT 2020 exam comes from CAT Progression: If f(5 + x) = f(5 – x) for every real x and f(x) = 0 has four distinct real roots, then the sum of the roots is

Find out by answering this question which tests an aspirant’s Quantitative Ability Skills:

CAT 2020 - Slot 1 - Quantitative Aptitude - Question 2: If f(5 + x) = f(5 - x) for every real x

Q.2 : If f(5 + x) = f(5 - x) for every real x and f(x) = 0 has four distinct real roots, then the sum of the roots is

1.  02. 403.  104.  20

Correct Answer: 20

Given f (5 + x) = f (5 – x)

When x = 1, f(6) = f(4)

When x = 2, f(7) = f(3)

Imagine a graph and while joining (6,4) and (7,3) it looks symmetrical about 5

Given 4 distinct real roots. Assume 12 as one of the roots.

f(12) = 0 –> Then f(5 + 7) = 0 which is same as f(5 – 7) = f(-2) = 0

So the roots are in the form (5 + k) and (5 – k) {This is one pair}

Sum of the roots = 5 + k + 5 – k = 10

We have 4 roots, So two pairs =10 + 10 = 20

Past Year Question Paper & Solutions

Counselling Session
By IIM Mentor

Go Social

Inspiring Education… Assuring Success!!
Ⓒ 2020 – All Rights Are Reserved

Free Content !!!
Signup now to get the All recent CAT Exam Paper with Solution... Subscribe below with your Email ID
Free Content !!!
Signup now to get the All recent CAT Exam Paper with Solution... Subscribe below with your Email ID