Relation between Roots and Coefficients for Quadratic
M N P ...
Question
M N P
x P N
--------------------
S Q N
N Q Q P x
--------------------------
N P M A N
Now, if 'P' stands for 6, 'M' for 4 and 'Q' for 5, then what is the difference between S and Q?
A
2
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B
3
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C
5
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D
8
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Solution
The correct option is B 3 Given, P = 6 , M = 4 and Q = 5. 4 N 6 x 6 N S 5 N N 5 5 6 x N 6 4 A N Where A = 5 + 6 = 11 so A = 1 & carry over 1 + S + 5 = 14, So S = 8 Therefore, 4 N 6 x 6 N 8 5 N +N 5 5 6 x N 6 4 1 N From the first row of multiplication it is clear that N × 6 = N
So, N can be either 2 or 4 or 6 or 8 or 0.
also, taking into consideration the second multiplication of N × N + carryover = 5 (in units place) , only N=2 fits
So, N = 2.
Also, N × 4 = 2 × 4 = 8
So, S = 8.
So difference between S and Q is 8 - 5 = 3 (option B)