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受欢迎的代数 >

4x^4-16x^3+7x^2+16x+4=0

解答

4 x^{4} - 16 x^{3} + 7 x^{2} + 16 x + 4 = 0

解答

x = 2, x = - \frac{1}{2}, x = \frac{5 + 41}{4}, x = \frac{5 - 41}{4}

+1

十进制

x = 2, x = - 0.5, x = 2.85078 \dots, x = - 0.35078 \dots

求解步骤

4 x^{4} - 16 x^{3} + 7 x^{2} + 16 x + 4 = 0

因式分解

4 x^{4} - 16 x^{3} + 7 x^{2} + 16 x + 4 : (x - 2) (2 x + 1) (2 x^{2} - 5 x - 2)

(x - 2) (2 x + 1) (2 x^{2} - 5 x - 2) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

x - 2 = 0 or 2 x + 1 = 0 or 2 x^{2} - 5 x - 2 = 0

解

x - 2 = 0 : x = 2

解

2 x + 1 = 0 : x = - \frac{1}{2}

解

2 x^{2} - 5 x - 2 = 0 : x = \frac{5 + 41}{4}, x = \frac{5 - 41}{4}

解为

x = 2, x = - \frac{1}{2}, x = \frac{5 + 41}{4}, x = \frac{5 - 41}{4}

作图

流行的例子

4x^4-65x^2+16=0

4 x^{4} - 65 x^{2} + 16 = 0

x^3-8x^2+12x+9=0

x^{3} - 8 x^{2} + 12 x + 9 = 0

z^{5} = 1

x^{4} + 3 x^{2} + 2 = 0

solvefor x,f*g=(x^2+1)^{10}

so l v e f or x, f \cdot g = (x^{2} + 1)^{10}