Quadratic equation Presented by: Abhishek Kumar
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Master table Signs visible in the X/Y's Question Equation Signs of actual values of X or Y Larger Value's Sign, Smaller Value's sign
Example x2 7x 12 0 y2-5y + 6-0 Soln: The signs of X's equation are and +, which means their solution is and . Both negative values. (Refer to the table) The signs of Y's equation are - and +, which means their solution values are and +. Both positive values. Obviously, X's possible values are both negative... And Y's possible values are both positive. Obviously, solution is X < Y
Example: x2 + 21x-32 = 0 y + 7y 12 0 Soln: The question's signs are and -, for both X & Y equations. Which means X and Y's values can be both positive or negative, as per master table... Answer is an instant CND (Can Not Determine. This takes hardly 5 seconds.
Example x2-12x+32 = 0 y-7y 12 0 Soln: The question's symbols are -, which means both values will be positive for each variable, x and y. x2-4x - 8x32 0 x(x-4)-4(x-8) = 0 X=4, X=8 y2-7y + 12=0 y2 -4y -3y+ 12 0 y(y-4)-3(y-4) = 0 Y= 4, Y = 4 So, X >= Y
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