Question

Ifa and b are the root of equation x^2+ax-b=0 then find a and b


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Answer 1

Step-by-step explanation:

${a}^{2} + {a}^{2} - b = 0 \\ \\ 2 {a}^{2} = b \\ {b}^{2} + ab - b = 0 \\ \\ {(2 {a}^{2}) }^{2} + a(2 {a)}^{2} - 2 {a}^{2} = 0 \\ \\ 4 {a}^{4} + 2 {a}^{3} - 2 {a}^{2} = 0 \\ \\ 4 {a}^{2} + 2a - 2 = 0 \\ \\ 2 {a}^{2} + a - 1 = 0 \\ \\ a = \frac{ - 1 + \sqrt{ {1}^{2} - 4} }{4} \\ \\ a = \frac{- 1 + i \sqrt{3} }{4} \: \: \: \: \: \: \frac{- 1 - i \sqrt{3} }{4} \\ \\ a = \frac{w}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{ - w}{2} \\ \\ \\ b = \frac{{w}^{2} }{2} \: \: \: \: \: \: \: \: \: \frac{ {w}^{2} }{2}$