Class 11 Science Mathematics Complex Numbers And Quadratic Equations Practice
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Algebra of complex numbers
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वर्गमूल के अंदर का व्यंजक गैर-ऋणात्मक होना चाहिए और हर शून्य नहीं हो सकता। अतः \(\frac{x-1}{x+2}\ge 0\) का हल चिन्ह-विधि से \(x<-2\) या \(x\ge1\) मिलता है। \(x=-2\) पर हर शून्य हो जाता है, इसलिए उसे शामिल नहीं किया जा सकता। अतः वास्तविक परिभाषा-क्षेत्र \((- infty,-2)\cup[1,\infty)\) है। परीक्षा-युक्ति: ऐसे प्रश्नों में अंश के शून्य और हर के शून्य को संख्या रेखा पर रखकर प्रत्येक अंतराल में चिन्ह जाँचें। / The expression under a square root must be non-negative, and the denominator cannot be zero. Thus, solve \(\frac{x-1}{x+2}\ge 0\). A sign analysis gives \(x<-2\) or \(x\ge1\). The point \(x=-2\) is excluded because it makes the denominator zero, so the real domain is \((- infty,-2)\cup[1,\infty)\). Exam tip: mark the zero of the numerator and the zero of the denominator on a number line, then test the sign in each interval.
