CAT 2023 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 5 : A quadratic equation x2+bx+c=0 has two real roots. If the difference between the reciprocals of the roots is 13, and the sum of the reciprocals of the squares of the roots is 59, then the largest possible value of (b+c) is
let α&β be the roots of x2+bx+c=0,
1α−1β=13
1α2+1β2=59
(1α−1β)2=19
49=2αβ
αβ=9/2
1α2+β2=α2+β2α2β2=(α+β)2−2αβ(αβ)2=59
(α+β)2=59(92)(92)+2(92)
(α+β)2=454+9=20+14=20.25
α+β=±4.5
α+β=−b1
b=−(α+β)
αβ=c1
c=αβ=4.5
b+c=−(α+β)+α
to maximize (b+c), we pick (α+β)=−4.5
b+c=−(−4.5)+4.5=9
So, the largest possible value of (b + c) is 9.
The question is " A quadratic equation x2+bx+c=0 has two real roots. If the difference between the reciprocals of the roots is 13, and the sum of the reciprocals of the squares of the roots is 59, then the largest possible value of (b+c) is "
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