This IIT JEE Maths lecture discusses a question from quadratic equations.
Find the set of all solutions of the equation:
2|y| - |2y-1 – 1| = 2y-1 + 1
The different cases for the range of y are taken. In the first case y is considered to range from -∞ to 0. In Mathematics, denotation is as important as the solution. There are numerous incidents of students losing marks because of incorrect denotations in solutions in case of school and board examinations. Also in entrance examinations if the notations in questions are incorrectly interpreted then the student is likely to proceed with the solution in a completely wrong direction. Here the notations of different brackets in the representation of intervals (range) are explained. Facts like this would be engraved in your minds with proper practice, thus remember to use IIT JEE test series, and AIEEE test series.
Because in the first case the value is negative, thus when the mod is removed a negative sign is introduced. On solving the equation, the value of y comes out as -1.
In the second case the value of y is 0 to 1 (Note the brackets in the solution). Note that in the 2nd mod, the values are negative despite the fact that the range of y is positive now. Care must be taken in cases like this because there is a chance of students making the mistake of taking the sign as positive. The value of y here is derived as 1.
The third case has the range of y from 1 to infinity. On solving it is observed that the case holds true for the whole range of 1 to infinity.
‘Quadratic Equations’ is a topic of Algebra that not only fetches direct questions but has widespread uses. It finds utility in solving different questions of Mathematics, Physics etc. Parabola for example can be represented in the form of a quadratic equation. It thus finds direct application in many fields of science including Engineering. After understanding the basics from proper IIT study material for Maths refer to IIT JEE test series and AIEEE test series to see the pattern of questions that make an appearance from this chapter.
One thing about IIT JEE is that it never fails to take the students by surprise. It always catches the students off-guard. Thus always prepare yourself for some unexpected twist. To brace yourself to face such situations, practice enough problems after strengthening your concepts. Choose IIT JEE study material, IIT JEE test series and AIEEE test series wisely. Online IIT study material in the form of videos can also be a great help.
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