CAT 2022 Question Paper | Quant Slot 3

CAT 2022 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 14 : If \((3+2 \sqrt{2})\) is a root of the equation \(a x^2+b x+c=0\), and \((4+2 \sqrt{3})\) is a root of the equation \(a y^2+m y+n=0\), where \(a, b, c, m\) and \(n\) are integers, then the value of \(\left(\frac{b}{m}+\frac{c-2 b}{n}\right)\) is

Video Explanation

Explanatory Answer

If \( ( 3 + 2 \sqrt { 2 } ) \) is a root of the equation \( a x ^ { 2 } + b x + c = 0 \), so is \( ( 3 - 2 \sqrt { 2 } ) \).
\( a x ^ { 2 } + b x + c = ( x - ( 3 + 2 \sqrt { 2 } ) ) ( x - ( 3 - 2 \sqrt { 2 } ) ) \)
\( a x ^ { 2 } + b x + c = x ^ { 2 } - 6 x + 1 \)
If \( ( 4 + 2 \sqrt { 3 } ) \) is a root of the equation \( a y ^ { 2 } + m y + n = 0 \), so is \( ( 4 - 2 \sqrt { 3 } ) \).
\( a y ^ { 2 } + m y + n = ( x - ( 4 + 2 \sqrt { 3 } ) ) ( x - ( 4 - 2 \sqrt { 3 } ) ) \)
\( a y ^ { 2 } + m y + n = x ^ { 2 } - 8 x + 4 \)
a = 1, b = -6, c = 1, m = -8, n = 4
Therefore \( \frac { b } { m } + \frac { c - 2 b } { n } \) = 4

The answer is '4'

Choice C is the correct answer.