Question

solve the equation x3-9x+28=0 by Cardon's method.​

Answer 1

Answer:

x = -4  & 2 ± i√3

Step-by-step explanation:

Solve the equation x³-9x+28=0

P(x) = x³ - 9x + 28

for x = -4

P(-4) = (-4)³ - 9(-4) + 28  = -64 + 36 + 28 = 0

=> x + 4 = 0

P(x) = g(x) q(x)

=>  x³ - 9x + 28 = (x + 4)(ax² + bx + c)

=> x³ - 9x + 28 = ax³ + (b + 4a)x²  + x(c + 4b) + 4c

Equating

a = 1

b + 4a = 0

=> b + 4 = 0

=> b = -4

c + 4b = -9

=> c + 4(-4) = -9

=> c = 7

or 28 = 4c => c = 7

ax² + bx + c  = x² -4x + 7

x² -4x + 7

=> x  =  (4 ± √16 - 28)/2  = (4 ± √-12)/2  = 2 ± i√3

Answer 2

Answer:

x^3-9x+28=0 cardons method