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If the quadratic expression \(x^2+px+16\) is a perfect square of a binomial, which statement about the possible values of \(p\) is correct?यदि द्विघात व्यंजक \(x^2+px+16\) किसी द्विपद का पूर्ण वर्ग है, तो \(p\) के संभावित मानों के बारे में कौन-सा कथन सही है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(p=8\) या \(p=-8\)\(p=8\) या \(p=-8\)
The expression must be \((x\pm4)^2\). Expanding gives \((x+4)^2=x^2+8x+16\) and \((x-4)^2=x^2-8x+16\), so \(p=\pm8\). Exam tip: take the square root of the constant term and check the middle term.\(x^2+px+16\) को \((x\pm4)^2\) होना चाहिए। विस्तार करने पर \((x+4)^2=x^2+8x+16\) और \((x-4)^2=x^2-8x+16\) मिलता है, अतः \(p=\pm8\)। परीक्षा टिप: स्थिर पद का वर्गमूल लेकर मध्य पद जाँचें।
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