Question

6. (a) By dividing through the equation x4 – 10x3 + 32x2 – 40x + 16 = 0 byx?

otherwise, solve the equation completely.
(b) Solve the equation x4 + x3 – 4x2-x + 1 = 0.
(c) Solve the following equation by dividing through by 4x2.
or

Answer 1

(x-2)²(x²-6x+4) or (x-2)²(x-(3+√5))(x-(3-√5))

Explanation:

x⁴ – 10x³ + 32x² – 40x + 16 = 0 divide equation

(x⁴-4x³+4x²)-(6x³-24x²+24x)+(4x²-16x+16) = 0

x²(x²-4x+4) - 6x(x²-4x+4) + 4(x²-4x+4) = 0

(x²-4x+4)(x²-6x+4) = 0

(x-2)²(x²-6x+4) = 0

x-2=0 or

x²-6x+4=0 ... roots: x = (6±√(-6)²-4*1*4) / 2 = (6±2√5) / 2 = 3±√5

x=2 or x=3±√5