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If \(\alpha\) and \(\beta\) are the zeroes of the polynomial \(3x^2+2x-1\), what is the value of \((\alpha+\beta)^2\)?यदि बहुपद \(3x^2+2x-1\) के शून्यक \(\alpha\) और \(\beta\) हैं, तो \((\alpha+\beta)^2\) का मान क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(\frac{4}{9}\)\(\frac{4}{9}\)
For a quadratic polynomial \(ax^2+bx+c\), the sum of its zeroes is \(-\frac{b}{a}\). Here, \(a=3\) and \(b=2\), so \(\alpha+\beta=-\frac{2}{3}\). Hence, \((\alpha+\beta)^2=\left(-\frac{2}{3}\right)^2=\frac{4}{9}\).द्विघात बहुपद \(ax^2+bx+c\) के शून्यकों का योग \(-\frac{b}{a}\) होता है। यहाँ \(a=3\) और \(b=2\), इसलिए \(\alpha+\beta=-\frac{2}{3}\)। अतः \((\alpha+\beta)^2=\left(-\frac{2}{3}\right)^2=\frac{4}{9}\)।
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