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If the sum of the zeroes of a monic quadratic polynomial is −4 and their product is 7, which polynomial is it?यदि किसी मोनिक द्विघात बहुपद के शून्यकों का योग −4 और गुणनफल 7 है, तो वह बहुपद कौन-सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(x^2+4x+7\)\(x^2+4x+7\)
If the zeroes are \(\alpha\) and \(\beta\), the monic quadratic is \(x^2-(\alpha+\beta)x+\alpha\beta\). Substituting their sum, −4, and product, 7, gives \(x^2-(-4)x+7=x^2+4x+7\).यदि शून्यक \(\alpha\) और \(\beta\) हैं, तो मोनिक द्विघात बहुपद \(x^2-(\alpha+\beta)x+\alpha\beta\) होता है। योग −4 और गुणनफल 7 रखने पर \(x^2-(-4)x+7=x^2+4x+7\) मिलता है।
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