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प्रश्न
Solve the equation
x4 + 3x3 – 3x – 1 = 0
उत्तर
(x – 1) and (x + 1) is a factor.
(x – 1)(x + 1)(x2 + 3x + 1) = 0
x – 1 = 0 or x + 1 = 0 or x2 + 3x + 1 = 0
x = 1 or x = – 1 or x2 + 3x = – 1
`(x + 3/2)^2 = - 1 + (3/2)^2`
`(x + 3/2)^2 = - 1 + (9/4)`
`(x + 3/2)^2 = 5/4`
`x + 3/2 = +- sqrt(5)/2`
x = `- 3/2 +- sqrt(5)/2`
x = `(- 3 +- sqrt(5))/2`
∴ Roots are `1, -1, (- 3 +- sqrt(5))/2`
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