An algebra problem by Ajay Dutta

Algebra Level 2

For two sets A = { ( x , y ) ∣ y = x 2 − a x + 48 } , B = { ( x , y ) ∣ y = 0 } , A=\{(x,y) \mid y=x^2-ax+48\}, B=\{(x,y) \mid y=0\}, what is the minimum value of a positive integer a a that satisfies n ( A ∩ B ) = 2 ? n(A \cap B)=2?

Note: n ( X ) n(X) is the number of the elements of the set X . X.

14 12 13 11

Ajay Dutta by Ajay Dutta , 24, India

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2 solutions

Its just the solving of the quadratic equation to find the two distinct roots (points where the parabola intersects the X axis).

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Arghyanil Dey
Apr 22, 2014

There are two elements in the intersection set of A&B. Certainly it indicates that there are two roots of the given equation 

                                                   X^2-aX+48=0

From this equation we get a=6+8=14(as we have to find the least value of a)

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