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受欢迎的代数 >

1+t-4t^2+t^3+t^4=0

解答

1 + t - 4 t^{2} + t^{3} + t^{4} = 0

解答

t = 1, t = \frac{- 3 + 5}{2}, t = \frac{- 3 - 5}{2}

+1

十进制

t = 1, t = - 0.38196 \dots, t = - 2.61803 \dots

求解步骤

1 + t - 4 t^{2} + t^{3} + t^{4} = 0

改写成标准形式

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

t^{4} + t^{3} - 4 t^{2} + t + 1 = 0

因式分解

t^{4} + t^{3} - 4 t^{2} + t + 1 : (t - 1)^{2} (t^{2} + 3 t + 1)

(t - 1)^{2} (t^{2} + 3 t + 1) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

t - 1 = 0 or t^{2} + 3 t + 1 = 0

解

t - 1 = 0 : t = 1

解

t^{2} + 3 t + 1 = 0 : t = \frac{- 3 + 5}{2}, t = \frac{- 3 - 5}{2}

解为

t = 1, t = \frac{- 3 + 5}{2}, t = \frac{- 3 - 5}{2}

作图

流行的例子

x^3+6x^2+11x+6=0

x^{3} + 6 x^{2} + 11 x + 6 = 0

x^{4} - x^{2} - 12 = 0

solvefor a,2(a^3+b^3)=7

so l v e f or a, 2 (a^{3} + b^{3}) = 7

y^{3} + y - 16 = 0

m^4-4m^3+8m^2-8m+4=0

m^{4} - 4 m^{3} + 8 m^{2} - 8 m + 4 = 0