Question

verification of given polynomials x^2+2√2x-6

Answer 1

x^2+2✓2x-6...
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Answer 2

$= {x}^{2} + 2 \sqrt{2}x - 6 \\ = {x}^{2} - \sqrt{2} x + 3 \sqrt{2} - 6 \\ = x(x - \sqrt{2} ) + 3 \sqrt{2} (x - \sqrt{2}) \\ = (x - \sqrt{2} )(x + 3 \sqrt{2}) \\ therefore \: x = \sqrt{2} \: \: \: \: \: x = - 3 \sqrt{2} \\ \alpha = \sqrt{2} \\ \beta = - 3 \sqrt{2} \\ \alpha + \beta = \sqrt{2} + (- 3 \sqrt{2} ) \\ = - 2 \sqrt{2} \\ \frac{ - b }{c} = \frac{ - 2 \sqrt{2} }{1} \\ = - 2 \sqrt{2} \\ ie \: alpha + \beta = \frac{ - b}{a} \\ \alpha \beta = \sqrt{2} \times - 3 \sqrt{2} \\ = - 6 \\ \frac{c}{a} = \frac{ - 6}{1} = - 6 \\ ie \: \alpha \beta = \frac{c}{a}$
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